Two end member models of how the high elevations in Tibet formed are (i) continuous thickening and widespread viscous flow of the crust and mantle of the entire plateau and (ii) time-dependent, localized shear between coherent lithospheric blocks. Recent studies of Cenozoic deformation, magmatism, and seismic structure lend support to the latter. Since India collided with Asia ∼55 million years ago, the rise of the high Tibetan plateau likely occurred in three main steps, by successive growth and uplift of 300- to 500-kilometer-wide crustal thrust-wedges. The crust thickened, while the mantle, decoupled beneath gently dipping shear zones, did not. Sediment infilling, bathtub-like, of dammed intermontane basins formed flat high plains at each step. The existence of magmatic belts younging northward implies that slabs of Asian mantle subducted one after another under ranges north of the Himalayas. Subduction was oblique and accompanied by extrusion along the left lateral strike-slip faults that slice Tibet's east side. These mechanisms, akin to plate tectonics hidden by thickening crust, with slip-partitioning, account for the dominant growth of the Tibet Plateau toward the east and northeast.