We propose that the Andes Cordillera formed by a “collision” between the trenchward-moving South American plate and the Nazca slab and subslab mantle. Resistance to trenchward motion, in the form of horizontal compressive normal stress, deforms South America's leading edge. The advancing continent also perturbs the subslab mantle flow field as mantle is displaced. This flow field, detected via shear-wave splitting, includes trench-parallel flow away from a central stagnation point and corner flow around the northern and southern ends of the continent. The corresponding spatial variation in applied stress accounts for the large-scale characteristics of Andean deformation: buckling at the stagnation point (maximum normal stress) forming the Central Andes and Bolivian orocline, and corner flow associated with the eastward motion of the Caribbean and Scotia plates. The high stresses required to form and maintain the Andes imply that South America's trenchward motion is primarily driven by deep mantle flow coupled to its base; no other driving force of sufficient magnitude is available. Similarities between North and South American plate motion history and large-scale Cordillera structure indicate that the western North American Laramide Rockies formed in a similar manner and that the North American plate is also driven westward by deep mantle flow. We infer that Atlantic spreading itself is similarly driven. By contrast, slab rollback in a closing ocean basin opens marginal basins at convergent margins, as in the western Pacific. We suggest that there is a causal link between the opening and closing of ocean basins and the formation of cordilleras and marginal basins. Cordillera formation occurs at the leading continental margin during the spreading phase of the Wilson cycle, whereas marginal basins form during the closing phase.