Sole structures for articles of footwear, including athletic footwear, include: (a) an outsole component; (b) a midsole component engaged with the outsole component, wherein the midsole component includes at least one opening or receptacle; (c) at least one fluid-filled bladder system or foam system provided in the opening or receptacle; and/or (d) a rigid plate system including one or more rigid plates overlaying the fluid-filled bladder or foam system(s). The rigid plate(s) may be fixed directly to the midsole component or the rigid plate(s) may rest on the fluid-filled bladder(s) or foam somewhat above the surface of the midsole component when the sole structure is in an uncompressed condition. Articles of footwear and methods of making sole structures and articles of footwear including such sole structures also are described.