초록 ▼

A shoe including a heel support integrally formed of a material different from the midsole material of a rear sole for supporting the foot of a user. The heel support includes a wall along at least one of the medial side of the shoe, the lateral side of the shoe and the rear of the shoe that extends

A shoe including a heel support integrally formed of a material different from the midsole material of a rear sole for supporting the foot of a user. The heel support includes a wall along at least one of the medial side of the shoe, the lateral side of the shoe and the rear of the shoe that extends vertically at least in part and includes at least one window through which at least a portion of the midsole material of the rear sole is exposed to and visible from outside the shoe.

대표청구항 ▼

We claim: 1. An assembly of footwear elements for use with an athletic shoe, the assembly comprising: an upper having an arch region and a heel region: a supporting structure: a flexible plate having an upper surface, a lower surface, an interior portion, and peripheral portions, at least a portion

We claim: 1. An assembly of footwear elements for use with an athletic shoe, the assembly comprising: an upper having an arch region and a heel region: a supporting structure: a flexible plate having an upper surface, a lower surface, an interior portion, and peripheral portions, at least a portion of the peripheral portions of the flexible plate being between at least a portion of the supporting structure and at least a portion of the heel region of the upper, at least a portion of the peripheral portions of the plate being restrained from movement relative to the interior portion of the plate in a substantially vertical direction so that the interior portion of the plate is capable of being deflected relative to the peripheral portions in a substantially vertical direction; a heel support integral with the flexible plate, the heel support having at least one upwardly-extending wall; and an arch bridge being integral with the flexible plate, the arch bridge extending from a position proximate a forward portion of the flexible plate. 2. The assembly according to claim 1, further comprising an element extending downwardly from the heel support of the assembly that at least partially defines a recess. 3. The assembly according to claim 2, wherein the recess of the heel support is configured to receive a rear sole. 4. The assembly according to claim 3, wherein the rear sole is detachable. 5. The assembly according to claim 3, wherein the rear sole is permanently attached and non-rotatable. 6. The assembly according to claim 3, wherein the rear sole is permanently fixed. 7. The assembly according to claim 1, further comprising at least one wall integral with the arch bridge proximate at least one of a medial side and a lateral side of the assembly and extending in an upwardly direction from the arch bridge, the at least one wall of the arch bridge being made of the same material as the flexible plate. 8. The assembly according to claim 1, when integrated into the athletic shoe, further comprises: at least one cushioning element extending below at least a portion of the flexible plate, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of a medial side and a lateral side of the shoe, the opening being in communication with the void to expose the interior portion of the plate from outside the shoe through the at least one opening and the void. 9. The assembly according to claim 8, further comprising at least another cushioning element that in part defines at least another opening, the the at least another opening being located on at least one of the medial side of the shoe, the lateral side of the shoe, and a rear of the shoe. 10. The assembly according to claim 9, wherein the at least another opening is located on the rear of the shoe. 11. The assembly according to claim 1, when integrated into the athletic shoe, is positioned such that the peripheral portion of the flexible plate is proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 12. The assembly according to claim 1, when integrated into the athletic shoe having a bottom and a rear sole having a bottom surface having at least two ground-engaging portions, wherein at least a portion of the plate is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 13. The assembly according to claim 1, when integrated into the athletic shoe having a heel region and a forward region, the one of the heel region and forward region having a bottom surface with a ground-engaging portion, wherein the arch bridge is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe. 14. The assembly according to claim 1, when integrated into the athletic shoe, the shoe comprises a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 15. The assembly according to claim 1, when integrated into the athletic shoe having a bottom, the assembly further comprising at least one substantially air-tight enclosure located between at least a portion of the flexible flexible plate and a portion of the bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 16. The assembly according to claim 1, when integrated into the athletic shoe having a bottom, the assembly further comprising a substantially air-tight enclosure located between at least a portion of the flexible plate and a portion of the bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 17. The assembly according to claim 1, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of the bottom of the shoe, one of the air-tight enclosures having having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 18. The assembly according to claim 1, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 19. The assembly according to claim 15, wherein the shoe further comprises a ground-engaging portion of the bottom surface including at least four portions each having a generally circular shape when viewed from beneath a bottom surface of a rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of the rear sole, at least two of the at least four circular-shaped portions being located proximate the medial side of the shoe and at least two of the at least four circular-shaped portions being located proximate the lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom surface of the rear sole having a diameter, the diameter of each of the circular-the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 20. The assembly according to claim 1, wherein the assembly is integrated into an athletic shoe designed for at least one of running, cross-training, basketball, and tennis. 21. The assembly according to claim 1, wherein the supporting structure is midsole. 22. The assembly according to claim 1, wherein the assembly is integrated into an exercise shoe. 23. The assembly according to claim 1, wherein the assembly is integrally formed from a one-piece thermoplastic material. 24. An assembly of footwear elements for use with an athletic shoe, the assembly comprising: a) an upper having an arch region and a heel region; b) a supporting structure; and c) a heel portion comprising: (i) a flexible plate having upper surface, a lower surface, an interior portion, and peripheral portions, the peripheral portions of the flexible plate being between at least a portion of the supporting structure and at least a portion of the heel region of the upper, at least a portion of the peripheral portions of the plate being restrained from movement relative to the interior portion of the plate in a substantially vertical direction so that the interior portion of the plate is capable of being deflected relative to the peripheral portions in a substantially vertical direction; and (ii) a rear sole support integral with the flexible plate, the rear sole support having at least one upwardly-extending wall; and d) an arch bridge integral with the heel portion, the arch bridge extending from a position proximate a forward portion of the heel portion. 25. The assembly according to claim 24, further comprising an element extending downwardly from the rear sole support of the assembly that at least partially defines a recess. 26. The assembly according to claim 25, wherein the recess of the rear sole support is configured to receive a rear sole. 27. The assembly according to claim 26, wherein the rear sole is detachable. 28. The assembly according to claim 26, wherein the rear sole is permanently attached and non-rotatable. 29. The assembly according to claim 26, wherein the rear sole is permanently fixed. 30. The assembly according to claim 24, further comprising at least one wall integral with the arch bridge proximate at least one of a medial side and a lateral side of the assembly and extending in an upwardly direction from the arch bridge, the at least one wall of the arch bridge being made of the same material as the flexible plate. 31. The assembly according to claim 24, when integrated into the athletic shoe, further comprises: at least one cushioning element extending below at least a portion of the flexible plate, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of a medial side and a lateral side of the shoe, the opening being in communication with the void to expose the interior portion of the plate from outside the shoe through the at least one opening and the void. 32. The assembly according to claim 31, further comprising at least another cushioning element that in part defines at least another opening, the at least another opening being located on at least one of the medial side of the shoe, the lateral side of the shoe, and a rear of the shoe. 33. The assembly according to claim 32, wherein the at least another opening is located on the rear of the shoe. 34. The assembly according to claim 24, when integrated into the athletic shoe, is positioned such that the peripheral portion of the flexible plate is proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 35. The assembly according to claim 24, when integrated into the athletic shoe having a bottom and a rear sole having a bottom surface having at least two ground-engaging portions, wherein at least a portion of the plate is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 36. The assembly according to claim 24, when integrated into the athletic shoe having a heel region and a forward region, each of the heel region and forward region having a bottom surface with a ground-engaging portion, wherein the arch bridge is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe. 37. The assembly according to claim 24, when integrated into the athletic shoe, the shoe comprises a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 38. The assembly according to claim 24, when integrated into the athletic shoe having a bottom, the assembly further comprising at least one substantially air-tight enclosure located between at least a portion of the flexible plate and a portion of the bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 39. The assembly according to claim 24, when integrated into the athletic shoe having a bottom, the assembly further comprising a substantially air-tight enclosure located between at least a portion of the flexible plate and a portion of the bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 40. The assembly according to claim 24, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 41. The assembly according to claim 24, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 42. The assembly according to claim 38, when integrated into the athletic shoe, the shoe further comprises a ground-engaging portion of the bottom surface including at least four portions each having a generally circular shape when viewed from beneath a bottom surface of a rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of the rear sole, at least two of the at least four circular-shaped portions being located proximate the medial side of the medial side of the shoe and at least two of the at least four circular-shaped portions being located proximate the lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom surface of the rear sole having a diameter, the diameter of each of the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 43. The assembly according to claim 24, wherein the assembly is integrated into an athletic shoe designed for at least one of running, cross-training, basketball, and tennis. 44. The assembly according to claim 24, wherein the supporting structure is midsole. 45. The assembly according to claim 24, wherein the assembly is integrated into an exercise shoe. 46. The assembly according to claim 24, Wherein the assembly is integrally formed from a one-piece thermoplastic material. 47. An assembly of footwear elements to be integrated into an athletic shoe, the assembly comprising: an upper having an arch region and a heel region; a supporting structure; a flexible region having an upper surface, a lower surface, an interior portion, and peripheral portions, the peripheral portions of the flexible region being between at least a portion of the supporting supporting structure and at least a portion of the heel region of the upper, at least a portion of the peripheral portions of the flexible region being restrained from movement relative to the interior portion of the flexible region in a substantially vertical direction so that the interior portion of the flexible region is capable of being deflected relative to the peripheral portions in a substantially vertical direction; at least one upwardly-extending wall; and an arch extension, the flexible region and the at least one upwardly-extending wall and the arch extension being integrally formed elements. 48. The assembly according to claim 47, further comprising an element extending downwardly from the flexible region that at least partially defines a recess. 49. The assembly according to claim 48, wherein the recess is configured to receive a rear sole. 50. The assembly according to claim 49, wherein the rear sole is detachable. 51. The assembly according to claim 49, wherein the rear sole is permanently attached and non-rotatable. 52. The assembly according to claim 49, wherein the rear sole is permanently fixed. 53. The assembly according to claim 47, further comprising at least one wall integral with the arch extension proximate at least one of a medial side and a lateral side of the assembly and extending in an upwardly direction from direction from the arch extension, the at least one wall of the arch extension being made of the same material as the flexible region. 54. The assembly according to claim 47, when integrated into the athletic shoe, further comprises: at least one cushioning element extending below at least a portion of the flexible region, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of a medial side and a lateral side of the shoe, the opening being in communication with the void to expose the interior portion of the flexible region from outside the shoe through the at least one opening and the void. 55. The assembly according to claim 54, further comprising at least another cushioning element that in part defines at least another opening, the at least another opening being located on at least one of the medial side of the shoe, the lateral side of the shoe, and a rear of the shoe. 56. The assembly according to claim 55, wherein the at least another opening is located on the rear of the shoe. 57. The assembly according to claim 47, when integrated into the athletic shoe, is positioned such that the peripheral portion of the flexible region is proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 58. The assembly according to claim 47, when integrated into the athletic shoe having a bottom and a rear sole having a bottom surface having at least two ground-engaging portions, wherein at least a portion of the flexible region is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 59. The assembly according to claim 47, when integrated into the athletic shoe having a heel region and a forward region, each of the heel region and forward region having a bottom surface with a ground-engaging portion, wherein the arch extension is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe. 60. The assembly according to claim 47, when integrated into the athletic shoe, the shoe comprises a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 61. The assembly according to claim 47, when integrated into the athletic shoe having a bottom, the assembly further comprising at least one substantially air-tight enclosure located between at least a portion of the flexible region and a portion of the bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 62. The assembly according to claim 47, when integrated into the athletic shoe having a bottom, the assembly further comprising a substantially air-tight enclosure located between at least a portion of the flexible region and a portion of the bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 63. The assembly according to claim 47, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible region and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 64. The assembly according to claim 47, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible region and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 65. The assembly according to claim 61, wherein the shoe further comprises a ground-engaging portion of the bottom surface including at least four portions each having a generally circular shape when viewed from beneath a bottom surface of a rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of the rear sole, at least two of the at least four circular-shaped portions being located proximate the medial side of the shoe and at least two of the at least four circular-shaped portions being located proximate the lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom surface of the rear sole having a diameter, the diameter of each of the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 66. The assembly according to claim 47, wherein the assembly is integrated into an athletic shoe designed for at least one of running, cross-training, basketball, and tennis. 67. The assembly according to claim 47, wherein the supporting structure is midsole. 68. The assembly according to claim 47, wherein the assembly is integrated into an exercise shoe. 69. The assembly according to claim 47, wherein the assembly is integrally formed from a one-piece thermoplastic material. 70. An assembly of footwear elements to be integrated into an athletic shoe, the assembly comprising: an upper having an arch region and a heel region; a supporting structure; a flexible region having an upper surface, a lower surface, an interior portion, and peripheral portions, the peripheral portions of the flexible region being between at least a portion of the supporting structure and at least a portion of the heel region of the upper, at least a portion of the peripheral portions of the flexible region being restrained from movement relative to the interior portion of the flexible region in a substantially vertical direction so that the interior portion of the flexible region is capable of being deflected relative to the peripheral portions in a substantially vertical direction; at least one upwardly-extending wall; and an arch extension, the flexible region and the at least one upwardly-extending wall and the arch extension being integrally formed elements. 71. The assembly according to claim 70, further comprising an element extending downwardly from the flexible region that at least partially defines a recess. 72. The assembly according to claim 71, wherein the recess is configured to receive a rear sole. 73. The assembly according to claim 72, wherein the rear sole is detachable. 74. The assembly according to claim 72, wherein the rear sole is permanently attached and non-rotatable. 75. The assembly according to claim 72, wherein the rear sole is permanently fixed. 76. The assembly according to claim 70, further comprising at least one wall integral with the arch extension proximate at least one of a medial side and a lateral side of the assembly and extending in an upwardly direction from the arch extension, the at least one wall of the arch extension being made of the same material as the flexible region. 77. The assembly according to claim 70, when integrated into the athletic shoe, further comprises: at least one cushioning element extending below at least a portion of the flexible region, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of a medial side and a lateral side of the shoe, the opening being in communication with the void to expose the interior portion of the flexible region from outside the shoe through the at least one opening and the void. 78. The assembly according to claim 77, further comprising at least another cushioning element that in part defines at least another opening, the at least another opening being located on at least one of the medial side of the the shoe, the lateral side of the shoe, and a rear of the shoe. 79. The assembly according to claim 78, wherein the at least another opening is located on the rear of the shoe. 80. The assembly according to claim 70, when integrated into the athletic shoe, is positioned such that the peripheral portion of the flexible region is proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 81. The assembly according to claim 70, when integrated into the athletic shoe having a bottom and a rear sole having a bottom surface having at least two ground-engaging portions, wherein at least a portion of the flexible region is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 82. The assembly according to claim 70, when integrated into the athletic shoe having a heel region and a forward region, each of the heel region and forward region having a bottom surface with a ground-engaging portion, wherein the arch extension is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe. 83. The assembly according to claim 70, when integrated into the athletic shoe, the shoe comprises a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 84. The assembly according to claim 70, when integrated into the athletic shoe having a bottom, the assembly further comprises at least one one substantially air-tight enclosure located between at least a portion of the flexible region and a portion of the bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 85. The assembly according to claim 70, when integrated into the athletic shoe, the assembly further comprising a substantially air-tight enclosure located between at least a portion of the flexible region and a portion of the bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 86. The assembly according to claim 70, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible region and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 87. The assembly according to claim 70, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible region and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 88. The assembly according to claim 84, wherein the shoe further comprises a ground-engaging portion of the bottom surface including at least four portions each having a generally circular shape when viewed from beneath a bottom surface of a rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of the rear sole, at least two of the at least four circular-shaped portions being located proximate the medial side of the shoe and at least two of the at least four circular-shaped portions being located proximate the lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom surface of the rear sole having a diameter, the diameter of each of the circular-the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 89. The assembly according to claim 70, wherein the assembly is integrated into an athletic shoe designed for at least one of running, cross-training, basketball, and tennis. 90. The assembly according to claim 70, wherein the supporting structure is midsole. 91. The assembly according to claim 70, wherein the assembly is integrated into an exercise shoe. 92. The assembly according to claim 70, wherein the assembly is integrally formed from a one-piece thermoplastic material. 93. An assembly of footwear elements to be integrated into an athletic shoe, the assembly comprising: an upper having an arch region and a heel region; a supporting structure; a flexible region having an upper surface, a lower surface, an interior portion, and peripheral portions, the peripheral portions of the flexible region being between at least a portion of the supporting structure and at least a portion of the heel region of the upper, at least a portion of the peripheral portions of the flexible region being restrained from movement relative to the interior portion of the flexible region in a substantially vertical direction so that the interior portion of the flexible region is capable of being deflected relative to the peripheral portions in a substantially vertical direction; at least one wall extending upwardly from a position proximate at least a portion of the periphery of the flexible region; and an arch extension extending from a position proximate and planar with a forward portion of the flexible region beyond an arch of a foot, the flexible region and the at least one upwardly-extending wall and the arch extension being integrally formed elements. 94. The assembly according to claim 93, further comprising an element extending downwardly from the flexible region that at least partially defines a recess. 95. The assembly according to claim 94, wherein the recess is configured to receive a rear sole. 96. The assembly according to claim 95, wherein the rear sole is detachable. 97. The assembly according to claim 95, wherein the rear sole is permanently attached and non-rotatable. 98. The assembly according to claim 95, wherein the rear sole is permanently fixed. 99. The assembly according to claim 93, further comprising at least one wall integral with the arch extension proximate at least one of a medial side and a lateral side of the assembly and extending in an upwardly direction from the arch extension, the at least one wall of the arch extension being made of the same material as the flexible region. 100. The assembly according to claim 93, when integrated into the athletic shoe, further comprises: at least one cushioning element extending below at least a portion of the flexible region, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of a medial side and a lateral side of the shoe, the opening being in communication with the void to expose the interior portion of the flexible region from outside the shoe through the at least one opening and the void. 101. The assembly according to claim 100, further comprising at least another cushioning element that in part defines at least another opening, the at least another opening being located on at least one of the medial side of the shoe, the lateral side of the shoe, and a rear of the shoe. 102. The assembly according to claim 101, wherein the at least another opening is located on the rear of the shoe. 103. The assembly according to claim 93, when integrated into the athletic shoe, is positioned such that the peripheral portion of the flexible region is proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 104. The assembly according to claim 93, when integrated into the athletic shoe having a bottom and a rear sole having a bottom surface having at least two ground-engaging portions, wherein at least a portion of the flexible region is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 105. The assembly according to claim 93, when integrated into the athletic shoe having a heel region and a forward region, each of the heel region and forward region having a bottom surface with a ground-engaging portion, wherein the arch extension is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe. 106. The assembly according to claim 93. , when integrated into the athletic shoe, the shoe comprises a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 107. The assembly according to claim 93, when integrated into the athletic shoe having a bottom, the assembly further comprising at least one substantially air-tight enclosure located between at least a portion of the flexible region and a portion of the bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 108. The assembly according to claim 93, when integrated into the athletic shoe having a bottom, the assembly further comprising a substantially air-tight enclosure located between at least a portion of the flexible region and a portion of the bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 109. The assembly according to claim 93, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible region and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 110. The assembly according to claim 93, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible region and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 111. The assembly according to claim 107, wherein the shoe further comprises a ground-engaging portion of the bottom surface including at least four portions each having a generally circular shape when viewed from beneath a bottom surface of a rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of the rear sole, at least two of the at least four circular-shaped portions being located proximate the medial side of the shoe and at least two of the at least four circular-shaped portions being located proximate the lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom surface of the rear sole having a diameter, the diameter of each of the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 112. The assembly according to claim 93, wherein the assembly is integrated into an athletic shoe designed for at least one of running, cross-training, basketball, and tennis. 113. The assembly according to claim 93, wherein the supporting structure is midsole. 114. The assembly according to claim 93, wherein the assembly is integrated into an exercise shoe. 115. An assembly of footwear elements to be integrated into an athletic shoe the assembly comprising: an upper having an arch region and a heel region; a supporting structure a flexible region having an upper surface, a lower surface, an interior portion, and peripheral portions, the peripheral portions of the flexible region being between at least a portion of the supporting structure and at least a portion of the heel region of the upper, at least a portion of the peripheral portions of the flexible region being restrained from movement relative to the interior portion of the flexible region in a substantially vertical direction so that the interior portion of the flexible region is capable of being deflected relative to the peripheral portions in a substantially vertical direction; at least one upwardly-extending wall; and an arch extension, the flexible region and the at least one upwardly-extending wall and the arch extension being integrally formed from a one-piece thermoplastic maternal. 116. The assembly according to claim 115, further comprising an element extending downwardly from the flexible region that at least partially defines defines a recess. 117. The assembly according to claim 116, wherein the recess is configured to receive a rear sole. 118. The assembly according to claim 117, wherein the rear sole is detachable. 119. The assembly according to claim 117, wherein the rear sole is permanently attached and non-rotatable. 120. The assembly according to claim 117, wherein the rear sole is permanently fixed. 121. The assembly according to claim 115, further comprising at least one wall integral with the arch extension proximate at least one of a medial side and a lateral side of the assembly and extending in an upwardly direction from the arch extension, the at least one wall of the arch extension being made of the same material as the flexible region. 122. The assembly according to claim 115, when integrated into the athletic shoe, further comprises: at least one cushioning element extending below at least a portion of the flexible region, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of the medial and lateral sides of the shoe, the opening being in communication with the void to expose the interior portion of the flexible region from outside the shoe through the at least one opening and the void. 123. The assembly according to claim 122, further comprising at least another cushioning element that in part defines at least another opening, the at least another opening being located on at least one of the medial side of the shoe, the lateral side of the shoe, and a rear of the shoe. 124. The assembly according to claim 123, wherein the at least another opening is located on the rear of the shoe. 125. The assembly according to claim 115, when integrated into the athletic shoe, is positioned such that the peripheral portion of the flexible region is proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 126. The assembly according to claim 115, when integrated into the athletic shoe having a bottom and a rear sole having a bottom surface having at least two ground-engaging portions, wherein at least a portion of the flexible region is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 127. The assembly according to claim 115, when integrated into the athletic shoe having a heel region and a forward region, each of the heel region and forward region having a bottom surface with a ground-engaging portion, wherein the arch extension is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe. 128. The assembly according to claim 115, when integrated into the athletic shoe, the shoe comprises a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 129. The assembly according to claim 115, when integrated into the athletic shoe having a bottom, the assembly further comprising at least one substantially air-tight enclosure located between at least a portion of the flexible flexible region and a portion of the bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 130. The assembly according to claim 115, when integrated into the athletic shoe having a bottom, the assembly further comprising a substantially air-tight enclosure located between at least a portion of the flexible region and a portion of the bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 131. The assembly according to claim 115, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible region and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 132. The assembly according to claim 115, integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible region and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 133. The assembly according to claim 129, wherein the shoe further comprises a ground-engaging portion of the bottom surface including at least four portions each having a generally circular shape when viewed from beneath a bottom surface of a rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of the rear sole, at least two of the at least four circular-shaped portions being located proximate the medial side of the shoe and at least two of the at least four circular-shaped portions being located proximate the lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom surface of the rear sole having a diameter, the diameter of each of the circular-the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 134. The assembly according to claim 115, wherein the assembly is integrated into an athletic shoe designed for at least one of running, cross-training, basketball, and tennis. 135. The assembly according to claim 115, wherein the supporting structure is midsole. 136. The assembly according to claim 115, wherein the assembly is integrated into an exercise shoe. 137. An assembly of footwear elements for supporting a foot in a shoe, the assembly comprising: an upper having an arch region and a heel region; a supporting structure; a heel support with a heel region; a plate positioned within the heel region of the heel support, the plate having an upper surface, a lower surface, an interior portion, and peripheral portions, the peripheral portions of the flexible plate being between at least a portion of the supporting structure and at least a portion of the heel region of the upper, at least a portion of the peripheral portions of the plate being restrained from movement relative to the interior portion of the plate in a substantially vertical direction so that the interior portion of the plate is capable of being deflected relative to the peripheral portions in a substantially vertical direction; an arch support extending from a position proximate and planar with a forward portion of the heel support forward beyond the arch of the foot; and a wall extending upwardly from a position proximate at least a portion of a periphery of the heel support; wherein the heel support, the arch support, and the wall are integrally formed from a one-piece thermoplastic material, the plate being permanently attached to the heel support and formed of the same thermoplastic material. 138. The assembly according to claim 137, wherein the heel support, the plate, the arch support, and the wall are integrally formed from the one-piece thermoplastic material. 139. The assembly according to claim 137, further comprising an element extending downwardly from the heel support that at least partially defines a recess. 140. The assembly according to claim 139, wherein recess of the heel support is configured to receive a rear sole. 141. The assembly according to claim 140, wherein the rear sole is detachable. 142. The assembly according to claim 140, wherein the rear sole is permanently attached and non-rotatable. 143. The assembly according to claim 140, wherein the rear sole is permanently fixed. 144. The assembly according to claim 137, further comprising at least one wall integral with the arch support proximate at least one of a medial side and a lateral side of the assembly and extending in an upwardly direction from the arch support, the at least one wall of the arch support being made of the same material as the plate. 145. The assembly according to claim 137, when integrated into the athletic shoe, further comprises: at least one cushioning element extending below at least a portion of the plate, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of a medial side and a lateral side of the shoe, the opening being in communication with the void to expose an interior portion of the plate from outside the shoe through the at least one opening and the void. 146. The assembly according to claim 145, further comprising at least another cushioning element that in part defines at least another opening, the at least another opening being located on at least one of the medial side of the shoe, the lateral side of the shoe, and a rear of the shoe. 147. The assembly according to claim 146, wherein the at least another opening is located on the rear of the shoe. 148. The assembly according to claim 137, when integrated into the athletic shoe, is positioned such that a peripheral portion of the plate is proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 149. The assembly according to claim 137, when integrated into the athletic shoe having a bottom and a rear sole having a bottom surface having at least two ground-engaging portions, wherein at least a portion of the plate is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 150. The assembly according to claim 137; when integrated into the athletic shoe having a heel region and a forward region, each of the heel region and forward region having a bottom surface with a ground-engaging portion, wherein the arch support is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe. 151. The assembly according to claim 137, when integrated into the athletic shoe, the shoe comprises a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 152. The assembly according to claim 137, when integrated into the athletic shoe having a bottom, the assembly further comprising at least one substantially air-tight enclosure located between at least a portion of the plate and a portion of the bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 153. The assembly according to claim 137, when integrated into the athletic shoe having a bottom, the assembly further comprising a substantially air-tight enclosure located between at least a portion of the plate and a portion of the bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 154. The assembly according to claim 137, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the plate and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosure being spaced apart from a vertical central axis of any other air-tight enclosure, the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 155. The assembly according to claim 137, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the plate and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 156. The assembly according to claim 152, wherein the shoe further comprises a ground-engaging portion of the bottom surface including at least four portions each having a generally circular shape when viewed from beneath a bottom surface of a rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of the rear sole, at least two of the at least four circular-shaped portions being located proximate the medial side of the shoe and at least two of the the at least four circular-shaped portions being located proximate the lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom surface of the rear sole having a diameter, the diameter of each of the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 157. The assembly according to claim 137, wherein the assembly is integrated into an athletic shoe designed for at least one of running, cross-training, basketball, and tennis. 158. The assembly according to claim 137, wherein the supporting structure is midsole. 159. The assembly according to claim 137, wherein the assembly is integrated into an exercise shoe. 160. An assembly of footwear elements to be integrated into an athletic shoe, the assembly comprising, an upper having an arch region and a heel region; a supporting structure; a heel support with a heel region; a plate positioned within the heel region of the heel support, the plate having a length extending along a central major axis of the assembly, the plate having an upper surface, a lower surface, an interior portion, and peripheral portions, the peripheral portions of the flexible plate being between at least a portion of the supporting structure and at least a portion of the heel region of the upper, at least a upper, at least a portion of the peripheral portions of the plate being restrained from movement relative to the interior portion of the plate in a substantially vertical direction so that the interior portion of the plate is capable of being deflected relative to the peripheral portions in a substantially vertical direction; an arch support extending from a position proximate and planar with a forward portion of the heel support, the arch support having a length extending along the central major axis of the assembly; and a wall extending upwardly from a position proximate at least a portion of the periphery of the heel support; wherein the heel support, the arch support, and the wall are integrally formed from a one-piece thermoplastic material and a ratio of the length of the arch support to the length of the plate is at least 1. 161. The assembly according to claim 159, wherein the heel support, the plate, the arch support, and the wall are integrally formed from the one-piece thermoplastic material. 162. The assembly according to claim 160, further comprising an element extending downwardly from the heel support of the assembly that at least partially defines a recess. 163. The assembly according to claim 162, wherein the recess of heel support is configured to receive a rear sole. 164. The assembly according to claim 163, wherein the rear sole is detachable. 165. The assembly according to claim 163, wherein the rear sole is permanently attached and non-rotatable. 166. The assembly according to claim 163, wherein the rear sole is permanently fixed. 167. The assembly according to claim 160, further comprising at least one wall integral with the arch support proximate at least one of a medial side and a lateral side of the assembly and extending in an upwardly direction from the from the arch support, the at least one wall of the arch support being made of the same material as the plate. 168. The assembly according to claim 160, when integrated into the athletic shoe, further comprises: at least one cushioning element extending below at least a portion of the plate, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of a medial and a lateral side of the shoe, the opening being in communication with the void to expose an interior portion of the plate from outside the shoe through the at least one opening and the void. 169. The assembly according to claim 168, further comprising at least another cushioning element that in part defines at least another opening, the at least another opening being located on at least one of the medial side of the shoe, the lateral side of the shoe, and a rear of the shoe. 170. The assembly according to claim 169, wherein he at least another opening is located on the rear of the shoe. 171. The assembly according to claim 160, when integrated into the athletic shoe, is positioned such that a peripheral portion of the plate is proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 172. The assembly according to claim 160, when integrated into the athletic shoe having a bottom and a rear sole having a bottom surface having at least two ground-engaging portions, wherein at least a portion of the plate is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 173. The assembly according to claim 160, when integrated into the athletic shoe having a heel region and a forward region, each of the heel region and forward region having a bottom surface with a ground-engaging portion, wherein the arch support is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe. 174. The assembly according to claim 160, when integrated into the athletic shoe, the shoe comprises a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 175. The assembly according to claim 160, when integrated into the athletic shoe having a bottom, the assembly further comprising at least one substantially air-tight enclosure located between at least a portion of the plate and a portion of the bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 176. The assembly according to claim 160, when integrated into the athletic shoe having a bottom, the assembly further comprising a substantially substantially air-tight enclosure located between at least a portion of the plate and a portion of the bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 177. The assembly according to claim 160, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the plate and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 178. The assembly according to claim 160, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the plate and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 179. The assembly according to claim 175, wherein the shoe further comprises a ground-engaging portion of the bottom surface including at least four portions each having a generally circular shape when viewed from beneath a bottom surface of a rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of the rear sole, at least two of the at least four circular-shaped portions being located proximate the medial side of the shoe and at least two of the at least four circular-shaped portions being located proximate the lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom surface of the rear sole having a diameter, the diameter of each of the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 180. The assembly according to claim 160, wherein the assembly is integrated into an athletic shoe designed for at least one of running, cross-training, basketball, and tennis. 181. The assembly according to claim 160, wherein the supporting structure is midsole. 182. The assembly according to claim 160, wherein the assembly is integrated into an exercise shoe. 183. An athletic shoe comprising: an upper having a heel region and an arch region; a sole; and an assembly of footwear elements positioned between at least a portion of the sole and at least a portion of the upper, the assembly comprising: (i) a flexible plate comprising at least a forward portion, an opposing rearward portion, an upper surface, a lower surface, an interior portion, and peripheral portions, the peripheral portions of the flexible plate being between the sole and at least a portion of the heel region of the upper, at least a portion of the peripheral portions of the plate being restrained from movement relative to the interior portion of the plate in a substantially vertical direction so that the interior portion of the plate is capable of being deflected relative to the peripheral portions in a substantially vertical direction, (ii) a heel support permanently attached to the flexible plate, and (iii) an arch bridge permanently attached to the flexible plate, the arch bridge extending from a position proximate a forward portion of the flexible plate, forward beneath at least a portion of the arch region of the upper; wherein the heel support comprises at least one upwardly-extending wall that at least partially surrounds at least a portion of the upper, and the sole and the upper form a one-piece structure. 184. The assembly according to claim 183, wherein the heel support, the flexible plate, and the arch bridge are integrally formed as a one-piece material. 185. The shoe according to claim 183, further comprising an element extending downwardly from the heel support that at least partially defines a recess. 186. The shoe according to claim 185, wherein the recess of the heel support is configured to receive a rear sole. 187. The shoe according to claim 186, wherein the rear sole is detachable. 188. The shoe according to claim 186, wherein the rear sole is permanently attached and non-rotatable. 189. The shoe according to claim 186, wherein the rear sole is permanently fixed. 190. The shoe according to claim 183, further comprising at least one wall integral with the arch bridge proximate at least one of a medial side and a lateral side of the assembly and extending in an upwardly direction from the arch bridge, the at least one wall of the arch bridge being made of the same material as the flexible plate. 191. The shoe according to claim 183, further comprising; at least one cushioning element extending below at least a portion of the flexible plate, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of a medial side and a lateral side of the shoe, the opening being in communication with the void to expose the interior portion of the plate from outside the shoe through the at least one opening and the void. 192. The shoe according to claim 191, further comprising at least another cushioning element that in part defines at least another opening, the at least another opening being located on at least one of the medial side of the shoe, the shoe, the lateral side of the shoe, and a rear of the shoe. 193. The shoe according to claim 192, , wherein the at least another opening is located on the rear of the shoe. 194. The shoe according to claim 183, wherein peripheral portions of the flexible plate are proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 195. The shoe according to claim 183, wherein at least a portion of the plate is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 196. The shoe according to claim 183, wherein the arch bridge is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe between a ground-engaging portion of a bottom surface in a heel region and a ground-engaging portion on the bottom surface in a forward region of the shoe. 197. The shoe according to claim 183, further comprising a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 198. The shoe according to claim 183, further comprising at least one substantially air-tight enclosure located between at least a portion of the flexible plate and a portion of the bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 199. The shoe according to claim 183, further comprising a substantially air-tight enclosure located between at least a portion of the flexible plate and a portion of the bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper of the shoe that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 200. The shoe according to claim 183, further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper of the shoe that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 201. The shoe according to claim 183, further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper of the shoe that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 202. The shoe according to claim 198, further comprising a ground-engaging portion of the bottom surface including at least four portions each having a generally circular shape when viewed from beneath the bottom surface of the rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of a rear sole, at least two of the at least four circular-shaped portions being located proximate a medial side of the shoe and at least two of the at least four circular-shaped portions being located proximate a lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom surface of the rear sole having a diameter, the diameter of each of the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 203. The shoe according to claim 183, wherein the shoe is an athletic shoe designed for at least one of running and cross-training. 204. The shoe according to claim 183, wherein the shoe is an athletic shoe designed for at least one of basketball and tennis. 205. The shoe according to claim 183, wherein the shoe is an exercise shoe. 206. The shoe according to claim 183, wherein the flexible plate, heel support and arch bridge are integrally formed from a one-piece thermoplastic material. 207. An athletic shoe comprising: (a) an upper having a heel region and an arch region: (b) a rear sole comprising: (1) a midsole, and (2) an outsole; (c) a flexible plate comprising at least an upper surface, a lower surface, an interior portion, and peripheral portions, the peripheral portions of the flexible plate being between the rear sole and at least a portion of the heel region of the upper, at least a portion of the peripheral portions of the plate being restrained from movement relative to the interior portion of the plate in a substantially vertical direction so that the interior portion of the plate is capable of being deflected relative to the peripheral portions in a substantially vertical direction; and (d) a heel support that restrains the downward lateral displacement of at least a part of the peripheral portion of the flexible plate relative to at least a substantial part of the interior portion of the flexible plate; the flexible plate, the heel support, and the sole form a one-piece structure; wherein the lower surface of the flexible plate is in air communication with the outside of the shoe. 208. The shoe according to claim 207, further comprising an element extending downwardly from the heel support that at least partially defines a recess. 209. The shoe according to claim 208, wherein the recess of the heel support is configured to receive the rear sole. 210. The shoe according to claim 209, wherein the rear sole is detachable. 211. The shoe according to claim 209, wherein the rear sole is permanently attached and non-rotatable. 212. The shoe according to claim 209, wherein the rear sole is permanently fixed. 213. The shoe according to claim 207, further comprising an arch bridge, the shoe having at least one wall integral with the arch bridge proximate at least one of a medial side and a lateral side of the shoe and extending in an upwardly direction from the arch bridge, the at least one wall of the arch bridge being made of the same material as the flexible plate. 214. The shoe according to claim 207, further comprising; at least one cushioning element extending below at least a portion of the flexible plate, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of a medial side and a lateral side of the shoe, the opening being in communication with the void to expose the interior portion of the plate from outside the shoe through the at least one opening and the void. 215. The shoe according to claim 214, further comprising at least another cushioning element that in part defines at least another opening, the at least another opening being located on at least one of the medial side of the shoe, the lateral side of the shoe, and a rear of the shoe. 216. The shoe according to claim 215, wherein the at least another opening is located on the rear of the shoe. 217. The shoe according to claim 207, wherein the peripheral portion of the flexible plate is proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 218. The shoe according to claim 207, wherein at least a portion of the plate is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 219. The shoe according to claim 213, wherein the arch bridge is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe between a ground-engaging portion of a bottom surface in a heel region and a ground-engaging portion on the bottom surface in a forward region of the shoe. 220. The shoe according to claim 207, further comprising a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 221. The shoe according to claim 207, further comprising at least one substantially air-tight enclosure located between at least a portion of the flexible plate and a portion of a bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 222. The shoe according to claim 207, further comprising a substantially air-tight enclosure located between at least a portion of the flexible plate and a portion of a bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper of the shoe that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 223. The shoe according to claim 207, further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of a bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper of the shoe that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 224. The shoe according to claim 207, further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of a bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of line between at least a portion of the bottom of the shoe and at least a portion of the upper of the shoe that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 225. The shoe according to claim 221, further comprising a ground-engaging portion of a bottom surface of the rear sole including at least four portions each having a generally circular shape when viewed from beneath the bottom surface of a rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of the rear sole, at least two of the at least four circular-shaped portions being located proximate the medial side of the shoe and at least two of the at least four circular-shaped portions being located proximate the lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom surface of the rear sole having a diameter, the diameter of each of the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 226. The shoe according to claim 207, wherein the shoe is an athletic shoe designed for at least one of running and cross-training. 227. The shoe according to claim 207, wherein the shoe is an athletic shoe designed for at least one of basketball and tennis. 228. The shoe according to claim 207, wherein the shoe is an exercise shoe. 229. An athletic shoe comprising: an upper having a heel region, and an arch region; one of a detachable rear sole, a rotatable rear sole, and a permanently attached, non-rotatable rear sole; a flexible plate having at least a forward portion, an opposing rearward portion, an upper surface, a lower surface, an interior portion, and peripheral portions, the peripheral portions of the flexible plate being between the rear sole and at least a portion of the heel region of the upper, at least a portion of the peripheral portions of the plate being restrained from movement relative to the interior portion of the plate in a substantially vertical direction so that the interior portion of the plate is capable of being deflected relative to the peripheral portions in a substantially vertical direction; a heel support being integral with the flexible plate; and an arch bridge integral with the flexible plate, the arch bridge extending from a position proximate the forward portion of the flexible plate, forward beneath at least a portion of the arch region of the upper; wherein the heel support comprises at least one upwardly-extending wall that at least partially surrounds at least one of a lateral side, a medial side and a rear end of the heel region of the upper. 230. The shoe according to claim 229, further comprising an element extending downwardly from the heel support that at least partially defines a recess. 231. The shoe according to claim 230, wherein the recess of the heel support is configured to receive a rear sole. 232. The shoe according to claim 231, wherein the rear sole is detachable. 233. The shoe according to claim 231, wherein the rear sole is permanently attached and non-rotatable. 234. The shoe according to claim 231, wherein the rear sole is permanently fixed. 235. The shoe according to claim 229, further comprising at least one wall integral with the arch bridge proximate at least one of a medial side and a lateral side of the shoe and extending in an upwardly direction from the arch bridge, the at least one wall of the arch bridge being made of the same material as the flexible plate. 236. The shoe according to claim 229, further comprising; at least one cushioning element extending below at least a portion of the flexible plate, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of a medial and a lateral side of the shoe, the opening being in communication with the void to expose the interior portion of the plate from outside the shoe through the at least one opening and the void. 237. The shoe according to claim 236, further comprising at least another cushioning element that in part defines at least another opening, the at least another opening being located on at least one of the medial side of the shoe, the lateral side of the shoe, and a rear of the shoe. 238. The shoe according to claim 237, wherein the at least another opening is located on the rear of the shoe. 239. The shoe according to claim 229, wherein the peripheral portion of the flexible plate is proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 240. The shoe according to claim 229, wherein at least a portion of the plate is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 241. The shoe according to claim 229, wherein the arch bridge is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe between a ground-engaging portion of a bottom surface in a heel region and a ground-engaging portion on the bottom surface in a forward region of the shoe. 242. The shoe according to claim 229, further comprising a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 243. The shoe according to claim 229, further comprising at least one substantially air-tight enclosure located between at least a portion of the flexible plate and a portion of a bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 244. The shoe according to claim 229, further comprising a substantially air-tight enclosure located between at least a portion of the flexible plate and a portion of a bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which Is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper of the shoe that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 245. The shoe according to claim 229, further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of a bottom of the shoe, one of the air-tight enclosures having a enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper of the shoe that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 246. The shoe according to claim 229, further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of a bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper of the shoe that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 247. The shoe according to claim 243, further comprising a ground-engaging portion of a bottom surface of the rear sole including at least four portions each having a generally circular shape when viewed from beneath the bottom surface of a rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of the rear sole, at least two of the at least four circular-shaped portions being located proximate the medial side of the shoe and at least two of the at least four circular-shaped portions being located proximate the lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom the bottom surface of the rear sole having a diameter, the diameter of each of the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 248. The shoe according to claim 229, wherein the shoe is an athletic shoe designed for at least one of running and cross-training. 249. The shoe according to claim 229, wherein shoe is an athletic shoe designed for at least one of basketball and tennis. 250. The shoe according to claim 229, wherein the shoe is an exercise shoe. 251. The shoe according to claim 229, wherein the flexible plate, heel support and arch bridge are integrally formed from a one-piece thermoplastic material. 252. An assembly of footwear elements for use with an athletic shoe, the assembly comprising: an upper having a heel region and an arch region; a midsole material; a flexible plate having an upper surface, a lower surface, an interior portion, and peripheral portions, the peripheral portions of the flexible plate being between at least a portion of the midsole material and at least a portion of the heel region of the upper, at least a portion of the peripheral portions of the plate being restrained from movement relative to the interior portion of the plate in a substantially vertical direction so that the interior portion of the elate is capable of being deflected relative to the peripheral portions in a substantially vertical direction; a heel support comprising at least one upwardly-extending wall, the heel support being permanently attached to the flexible plate; the midsole material being located beneath the flexible plate, a portion of the midsole material having a width as measured from an exterior surface along a medial side of the midsole material to an opposing exterior surface along a lateral side of the midsole material; and the heel region of the upper having a width as measured from an exterior surface along a medial side of the heel region of the upper to an opposing exterior surface along a lateral side of the heel region of the upper, the width of the portion of the midsole material being greater than the width of the heel region of the upper. 253. The assembly according to claim 252, wherein the heel support and the flexible plate are integrally formed as a one-piece material. 254. The assembly according to claim 252, further comprising an element extending downwardly from the heel support that at least partially defines a recess. 255. The assembly according to claim 254, wherein the recess of the heel support is configured to receive a rear sole. 256. The assembly according to claim 255, wherein the rear sole is detachable. 257. The assembly according to claim 255, wherein the rear sole is permanently attached and non-rotatable. 258. The assembly according to claim 255, wherein the rear sole is permanently fixed. 259. The assembly according to claim 255, further comprising an arch bridge, the assembly having at least one wall integral with the arch bridge bridge proximate at least one of a medial side and a lateral side of the assembly and extending in an upwardly direction from the arch bridge, the at least one wall of the arch bridge being made of the same material as the flexible plate. 260. The assembly according to claim 252, when integrated into the athletic shoe, further comprises; at least one cushioning element extending below at least a portion of the flexible plate, the at least one cushioning element having: (i) an exterior surface that is at least in part visible from outside the shoe, and (ii) an interior surface that at least partially defines a void, wherein the at least one cushioning element in part defines at least one opening on at least one of a medial side and a lateral side of the shoe, the opening being in communication with the void to expose the interior portion of the plate from outside the shoe through the at least one opening and the void. 261. The assembly according to claim 260, further comprising at least another cushioning element that in part defines at least another opening, the at least another opening being located on at least one of the medial side of the shoe, the lateral side of the shoe, and a rear of the shoe. 262. The assembly according to claim 261, wherein the at least another opening is located on the rear of the shoe. 263. The assembly according to claim 252, when integrated into the athletic shoe, is positioned such that the peripheral portion of the flexible plate is proximate with a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 264. The assembly according to claim 252, when integrated into the athletic shoe having a bottom and a rear sole having a bottom surface having at least two ground-engaging portions, wherein at least a portion of the plate is visible from the bottom of the shoe between the at least two ground engaging portions and being in air communication with the air outside the shoe. 265. The assembly according to claim 259, when integrated into the athletic shoe having a heel region and a forward region, each of the heel region and forward region having a bottom surface with a ground-engaging portion, wherein the arch bridge that is non-ground engaging, in air communication with the outside of the shoe, and at least in part visible from beneath the shoe. 266. The assembly according to claim 252, when integrated into the athletic shoe, the shoe comprises a ground-engaging portion of a bottom surface including a substantially planar portion and at least one non-planar portion, the at least one non-planar portion positioned proximate the perimeter of the bottom surface and inclined upwardly in a direction toward the perimeter of the bottom surface from another portion of the bottom surface, the at least one non-planar portion having an outer edge proximate a portion of the perimeter of the bottom surface and proximate a forward portion of a rear sole. 267. The assembly according to claim 252, when integrated into the athletic shoe having a bottom, the assembly further comprising at least one substantially air-tight enclosure located between at least a portion of the flexible plate and a portion of the bottom of the shoe, the at least one air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the at least one air-tight enclosure, an exterior surface, and an interior chamber having a height parallel with the vertical central axis, the interior chamber having a top portion, a bottom portion, and a middle portion connecting the top and bottom portions, the interior chamber having a transverse-cross-sectional dimension in a plane generally perpendicular to the vertical central axis that is variable in the middle portion along at least a portion of the height of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 268. The assembly according to claim 252, when integrated into the athletic shoe having a bottom, the assembly further comprising a substantially air-tight enclosure located between at least a portion of the flexible plate and a portion of the bottom of the shoe, the air-tight enclosure having a top, a bottom, a vertical central axis passing through the top and the bottom of the air-tight enclosure, an exterior surface, and an interior chamber, the interior chamber having a height parallel with the vertical central axis of the air-tight enclosure, the interior chamber being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, at least a portion of the exterior surface being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 269. The assembly according to claim 252, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the the exterior surface of the at least one sidewall having at least two portions integral with the exterior surface and non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other in a direction away from the vertical central axis of the one of the air-tight enclosures, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 270. The assembly according to claim 252, when integrated into the athletic shoe having a bottom, the assembly further comprising a plurality of substantially air-tight enclosures located between at least a portion of the flexible plate and a portion of the bottom of the shoe, one of the air-tight enclosures having a top, a bottom, a vertical central axis passing through the top and the bottom of the one of the air-tight enclosures, at least one sidewall connecting the top and the bottom of the one of the air-tight enclosures and having an exterior surface and an interior surface, the one of the air-tight enclosures having a single interior chamber defined at least in part by the interior surface of the at least one sidewall, the interior chamber of the one of the air-tight enclosures being the only chamber any portion of which is located on any line between at least a portion of the bottom of the shoe and at least a portion of the upper that is generally parallel with the vertical central axis and passes through any portion of the interior chamber, the vertical central axis of the one of the air-tight enclosures being spaced apart from a vertical central axis of any other air-tight enclosure, the interior surface of the at least one sidewall having at least two portions each of which is substantially non-parallel with the vertical central axis, at least one of the portions being oriented at least in part in a direction toward a portion of the upper, another of the at least two portions being oriented at least in part in a direction toward a direction toward a portion of the bottom of the shoe, the at least two portions converging toward each other, permanently connecting with each other and forming an apex, at least a portion of the exterior surface of the at least one sidewall being exposed to and visible from at least one of a medial side of the shoe, a lateral side of the shoe, and a rear of the shoe. 271. The assembly according to claim 267, wherein the shoe further comprises a ground-engaging portion of a bottom surface of a rear sole including at least four portions each having a generally circular shape when viewed from beneath the bottom surface of a rear sole, each of the at least four circular-shaped portions having an outer edge proximate at least a portion of the perimeter of the bottom surface of the rear sole, at least two of the at least four circular-shaped portions being located proximate the medial side of the shoe and at least two of the at least four circular-shaped portions being located proximate the lateral side of the shoe, each of the at least four circular-shaped portions having a center, the centers of four of the at least four circular-shaped portions forming the corners of a quadrilateral having two opposed sides that are generally parallel with a major longitudinal axis of the shoe, each of the circular-shaped portions of the bottom surface of the rear sole having a diameter, the diameter of each of the circular-shaped portions being less than one-half the maximum width of the bottom surface of the rear sole as measured on a line substantially perpendicular to the major longitudinal axis of the shoe from a point on the medial side of the shoe to a point on the lateral side of the shoe. 272. The assembly according to claim 252, wherein the assembly is integrated into an athletic shoe, designed for at least one of running and cross-training. 273. The assembly according to claim 252, wherein the assembly is integrated into an athletic shoe designed for at least one of basketball and tennis. 274. The assembly according to claim 252, wherein the assembly is integrated into an exercise shoe. 275. The assembly according to claim 252, wherein the assembly is integrally formed from a one-piece thermoplastic material. 276. The assembly according to claim 252, wherein the downward lateral displacement of at least a part of the peripheral portion of the flexible plate is relative to at least a substantial part of the interior portion of the flexible plate. 277. An assembly of footwear elements for use with an athletic shoe, the assembly comprising: a shoe upper having a front, a back, a forward region, a heel region, a midfoot region located between the forward region and the heel region, and a mid-longitudinal axis, the heel region of the upper having a medial side, a lateral side, a rear, and a vertical central axis a heel support adapted to be adjacent the heel region of the upper, the heel support having a medial side adapted to be proximate the medial side of the heel region of the upper, a lateral side adapted to be proximate the lateral side of the heel region of the upper, and a rear, the heel support including at least one permanently attached wall extending in a generally downward direction from the heel support, at least a portion of the wall being proximate at least one of the medial side of the heel support, the lateral side of the heel support, and the rear of the heel support and being exposed to and visible from the outside of the assembly; a flexible member located beneath at least a portion of the heel region of the upper, the flexible member having an upper surface, a lower surface, an interior portion, and peripheral portions, at least a portion of the peripheral portions of the flexible member being between at least a portion of the wall of the heel support and at least a portion of the heel region of the upper, at least a portion of the peripheral portions being restrained from movement relative to the interior portion of the flexible member in a substantially vertical direction so that the interior portion is capable of being deflected relative to the peripheral portions in a substantially vertical direction, at least a portion of the peripheral portions being proximate the medial side of the heel support and at least a portion of the peripheral portions being proximate the lateral side of the heel support; an arch bridge located beneath at least a portion of the midfoot region of the upper to support an arch region of the user's foot, the arch bridge having an upper surface, a lower surface, a medial side and a lateral side; and the heel support and the arch bridge of the assembly being permanently attached to each other, the flexible member being permanently attached to the heel support. 278. The assembly of claim 277, wherein the heel support has A permanently attached wall extending in a generally upward direction. 279. The assembly of claim 278, wherein at least a portion of the upwardly extending wall is proximate at least one of the medial side of the heel support, the lateral side of the heel support, and the rear of the heel support and is exposed to and visible from the outside of the assembly. 280. The assembly of claim 227, wherein the interior portion of the flexible member is positioned over a void. 281. The assembly of claim 280, wherein the void is defined at least in part by a portion of the at least one generally downward extending wall. 282. The assembly of claim 281, wherein the interior portion of the flexible member is in air communication with the void. 283. The assembly of claim 281, wherein the interior portion of the flexible member is capable of being deflected toward the void. 284. The assembly of claim 281, wherein the interior portion of the flexible member is capable of being deflected into the void. 285. The assembly of claim 282, wherein the interior portion of the flexible member is capable of being deflected into the void. 286. The assembly of claim 281, wherein the at least one generally downward extending wall has at least one opening therethrough. 287. The assembly of claim 281, wherein the at least one generally downward extending wall has at least two openings therethrough, one of the at least two openings being located on the lateral side of the heel support and one of the at least two openings being located on one of the medial side and the rear of the heel support. 288. The assembly of claim 281, wherein the at least one generally downward extending wall has at least three openings therethrough, one of the at least three openings being located on the lateral side of the heel support, one of the at least three openings being located on the medial side of the heel support, and one of the at least three openings being located on the rear of the heel support. 289. The assembly of claim 281, wherein the at least one generally downward extending wall has at least four openings therethrough, one of the at least four openings being located on the lateral side of the heel support, one of the at least four openings being located on the medial side of the heel support, and one of the at least four openings being located on the rear of the heel support. 290. The assembly of claim 286, wherein the void is in air communication with the outside of the assembly through the at least one opening. 291. The assembly of claim 290, wherein the interior portion of the flexible member is in air communication with the void and with the outside of the assembly through the at least one opening. 292. The assembly of claim 277, wherein the flexible member is supported at the peripheral portions by the heel support. 293. The assembly of claim 277, wherein the flexible member is supported about a substantial portion of the peripheral portions by the heel support. 294. The assembly of claim 277, wherein the flexible member is supported about substantially the entire peripheral portions by the heel support. 295. The assembly of claim 277, wherein the flexible member is supported by the heel support at a point proximate the medial side and at a point proximate the lateral side of the heel support. 296. The assembly of claim 277, wherein the flexible member is supported by the heel support along a forward facing portion and along a rearward facing portion of the heel support. 297. The assembly of claim 277, wherein the flexible member is supported by the heel support at a point proximate the medial side of the heel support, at a point proximate the lateral side of the heel support, along a forward facing portion of the heel support and along a rearward facing portion of the heel support. 298. The assembly of claim 277, wherein the arch bridge has proximate at least one of its medial side and its lateral side at least one wall integral with the arch bridge and extending in a generally downward direction, the wall having an exterior surface, at least a portion of the exterior surface being exposed to and visible from the outside of the assembly. 299. The assembly of claim 277, wherein the arch bridge has proximate at least one of its medial side and its lateral side at least one wall integral with the arch bridge and extending in a generally upward direction, the wall having an exterior surface, at least a portion of the exterior surface being exposed to and visible from the outside of the assembly. 300. The assembly of claim 277, further including a forward sole located beneath the forward region of the upper, the forward sole including at least one inflated cushion. 301. The assembly of claim 277, further including a forward sole located beneath the forward region of the upper, the forward sole including at least one substantially air-tight enclosure. 302. The assembly of claim 277, further including a forward sole located beneath the forward region of the upper, the forward sole including at least one air bladder. 303. The assembly of claim 277, further including at least one rib integrally formed with the flexible member and located on the lower surface of the the flexible member. 304. The assembly of claim 303, wherein the at least one rib includes at least two ribs. 305. The assembly of claim 303, wherein the at least one rib includes at least three ribs. 306. The assembly of claim 303, wherein the at least one rib includes at least four ribs. 307. The assembly of claim 277, wherein the flexible member has at least one hole therethrough. 308. The assembly of claim 307, wherein the lower surface of the flexible member is in air communication with the heel region of the upper through the at least one hole. 309. The assembly of claim 307, wherein the at least one hole is through the approximate center of the flexible member. 310. The assembly of claim 307, wherein the at least one hole has a perimeter, the perimeter of the hole surrounding the vertical central axis of the heel region of the upper. 311. The assembly of claim 277, wherein the flexible member is approximately planar. 312. The assembly of claim 227, wherein at least a portion of the upper surface of the flexible member is convex in shape. 313. The assembly of claim 227, wherein at least a portion of the upper surface of the flexible member is concave in shape. 314. The assembly of claim 277, wherein at least one portion of a cross section of the flexible member parallel to the mid-longitudinal axis of the upper defines a curve in a direction generally from the back of the upper toward the front of the upper. 315. The assembly of claim 277, wherein at least one portion of a cross section of the flexible member perpendicular to the mid-longitudinal axis of axis of the upper defines a curve in a direction generally from the medial side of the heel region of the upper toward the lateral side of the heel region of the upper. 316. The assembly of claim 277, wherein at least one portion of a cross section of the flexible member parallel to the mid-longitudinal axis of the upper defines a curve in a direction generally from the back of the upper toward the front of the upper, and another cross section of the flexible member perpendicular to the mid-longitudinal axis of the upper defines a second curve generally in a direction from the medial side of the heel region of the upper toward the lateral side of the heel region of the upper. 317. The assembly of claim 277, wherein the flexible member has a thickness, the thickness of the flexible plate varying as measured along a line parallel to the mid-longitudinal axis of the upper. 318. The assembly of claim 277, wherein the flexible member has a thickness, the thickness of the flexible member varying as measured along a line perpendicular to the mid-longitudinal axis of the upper. 319. The assembly of claim 277, wherein a portion of the interior portion of the flexible member is thicker than a portion of the peripheral portions of the flexible plate. 320. The assembly of claim 277, wherein a portion of the interior portion of the flexible member is thinner than a portion of the peripheral portions of the flexible member. 321. The assembly of claim 277, wherein the heel support is formed of a material, the arch bridge being formed of the same material as the heel support. 322. The assembly of claim 277, wherein the arch bridge and the heel support are molded as a one-piece construction. 323. The assembly of claim 277, wherein the lower surface of the arch bridge extends below at least a substantial portion of the midfoot region of the upper. 324. The assembly of claim 277, wherein the lower surface of the arch bridge extends below substantially the entire midfoot region of the upper. 325. The assembly of claim 277, wherein the assembly is a portion of a complete shoe, the complete shoe has a bottom, and the lower surface of the flexible member is in air communication with the outside of the complete shoe through the bottom of the complete shoe. 326. The assembly of claim 277, wherein the assembly is a portion of a complete shoe, at least one substantially air-tight enclosure is located beneath at least one of the forward region and the heel region of the upper, and no portion of the substantially air-tight enclosure is located below the interior portion of flexible member along the vertical central axis of the heel region of the upper. 327. The assembly of claim 277, wherein the assembly is a portion of a complete shoe, the vertical central axis of the heel region of the upper passes through the interior portion of the flexible member, and no portion of any substantially air-tight enclosure is located along the vertical central axis below the interior portion of the flexible member. 328. The assembly of claim 277, wherein the assembly is a portion of a complete shoe, the complete shoe includes at least one inflated cushion, and the lower surface of the flexible member is spaced apart from the at least one inflated cushion in the complete shoe. 329. The assembly of claim 278, wherein the upwardlv extending wall is integral with the heel support. 330. The assembly of claim 277, wherein the downwardly extending wall is integral with the heel support. 331. The assembly of claim 277, wherein the heel support, the arch bridge, and the flexible member are integrally formed. 332. The assembly of claim 277, wherein the heel support, flexible member, and arch bridge are made of the same material. 333. The assembly of claim 277, wherein the assembly is a portion of a complete shoe, the complete shoe has a bottom, and the lower surface of the arch bridge is at least in part exposed to and visible from the bottom of the shoe. 334. The assembly of claim 303, wherein the assembly is a portion of a complete shoe, the complete shoe has a bottom, and the at least one rib is exposed to and visible from the bottom of the complete shoe.