Shear-wave splitting of S and SKS phases reveals the anisotropy and strain field of the mantle beneath the subducting Nazca plate, Cocos plate, and the Caribbean region. These observations can be used to test models of mantle flow. Two-dimensional entrained mantle flow beneath the subducting Nazca slab is not consistent with the data. Rather, there is evidence for horizontal trench-parallel flow in the mantle beneath the Nazca plate along much of the Andean subduction zone. Trench-parallel flow is attributable to retrograde motion of the slab, the decoupling of the slab and underlying mantle, and a partial barrier to flow at depth, resulting in lateral mantle flow beneath the slab. Such flow facilitates the transfer of material from the shrinking mantle reservoir beneath the Pacific basin to the growing mantle reservoir beneath the Atlantic basin. Trench-parallel flow may explain the eastward motions of the Caribbean and Scotia sea plates, the anomalously shallow bathymetry of the eastern Nazca plate, the long-wavelength geoid high over western South America, and it may contribute to the high elevation and intense deformation of the central Andes.