Sole structures for articles of footwear, including athletic footwear, include a relatively soft and lightweight foam midsole component partially covered by at least one more rigid and/or dense cage (protective) component(s) and/or other protective component(s). The sole structure may include a first polymeric foam member, wherein an exposed outer edge of the first polymeric foam member includes a billows structure that extends continuously from a medial midfoot or forefoot area of the first polymeric foam member proximate to a lateral midfoot or forefoot area of the first polymeric foam member, and wherein the billows structure includes billow outer ridges connected by billow interstitial areas located between adjacent billow outer ridges.