Sole structures for articles of footwear, including athletic footwear, include: (a) a lightweight foam midsole component for supporting the foot; and (b) a plurality of heavier and/or denser cage components covering selected areas of the midsole component. Spaces are provided between the cage components. These spaces may be sized, shaped, and oriented to define and/or correspond to flexion lines of the foot and/or to produce a more natural flex motion to the sole. The soles additionally may include one or more outsole components, e.g., on bottom surface(s) of the cage component(s) and/or the foam midsole. These sole structures may be engaged with an upper to form a shoe. The uppers may include one or more lace receiving openings supported by elongated wire or textile components. Methods of making footwear including such uppers and/or sole structures also are described.