How the collision between India and Asia is related to processes deeper in the mantle is unclear. Here we compare geological reconstructions of block motions within Asia since ≈50 Ma with the tomographically imaged three-dimensional (3-D) morphology of subducted lithosphere to obtain insight into the spatiotemporal evolution of mantle structure. Past positions of the convergent margin show remarkable similarities with slab geometry at specific depths. The striking change in slab geometry from a linear structure beneath 1100 km to an increasingly distorted shape at depths of less than 700 km results from collision. The slab contours match the progressive deformation of Asia's margin, including India's indentation and Sundaland's extrusion. Ever since the onset of collision, the Indian plate appears to have overridden its own sinking mantle and it does not seem, at present, to underthrust Tibet significantly north of the Zangbo suture. If correct, this observation would provide further evidence against models of plateau build-up involving Indian lithosphere. The tomographic images beneath India confirm that Asian deformation has absorbed at least ≈1500 km of convergence since collision began. From the match between the southeastward motion of Sundaland between 40 and 20 Ma and the principal change in slab structure between 700 and 1100 km depths, we infer that lateral advection in the mantle is small and that the sinking rate beneath Sunda was ∼2 cm/yr in the lower mantle and ∼5 cm/yr above the transition zone.