We discuss the relationships between Andean shortening, plate velocities at the trench, and slab geometry beneath South America. Although some correlation exists between the convergence velocity and the westward motion of South America on the one hand, and the shortening of the continental plate on the other hand, plate kinematics neither gives a satisfactory explanation to the Andean segmentation in general, nor explains the development of the Bolivian orocline in Paleogene times. We discuss the Cenozoic history of horizontal slab segments below South America, arguing that they result from the subduction of oceanic plateaus whose effect is to switch the buoyancy of the young subducting plate to positive. We argue that the existence of horizontal slab segments, below the Central Andes during Eocene-Oligocene times, and below Peru and North-Central Chile since Pliocene, resulted (1) in the shortening of the continental plate interiors at a large distance from the trench, (2) in stronger interplate coupling and ultimately, (3) in a decrease of the trenchward velocity of the oceanic plate. Present-day horizontal slab segments may thus explain the diminution of the convergence velocity between the Nazca and South American plates since Late Miocene.