A sole structure for an article of footwear comprises a midsole system with a plurality of cushioning units, each having multiple cushioning layers configured to work together as a system to absorb a compressive load, such as a dynamic compressive load due to impact with the ground, in stages of progressive cushioning according to the relative stiffness values of the layers. Various midsole systems disclosed include isolated cushioning units, linked cushioning units, sole layers having stanchions interfacing with the midsole system, midsole systems with sole layers having keyed and unkeyed portions overlying a bladder, and midsole systems with vertically-stacked cushioning units disposed in inverted relationship to one another.