The interaction of neighboring subducting lithospheres is a characteristic feature of many tectonically complex areas. Here we use numerical modeling to study the interactions between two oppositely dipping, adjacent subducting lithospheres and to understand their impact on the subduction evolution, mantle flow, and stress propagation through the mantle. As slabs subduct, rollback, and approach, they strongly affect each other if plate edges are at distances <~600 km. In this case the mantle flow around slabs combines into a single, large convective cell, trench migration is delayed, and stress increases progressively with decreasing slabs distance. The stress increases at depth as the slabs approach each other, and it shallows up to the near surface as the slabs diverge. A similar setting, with two neighboring slabs migrating and passing each other, is found in areas such as the Alps-Apennines (Europe) and the Ryukyu-Manila subduction zones around Taiwan, where the arcuate trenches suggest the controls of deep slab interactions.