In subduction zones, the effects of plate kinematics on the geometry of the slab, and its consequences on the tectonic regime of the overriding plate have been largely debated during the last decades. In the Andes, both the absolute westward motion of the South American plate and the convergence velocity have been invoked to contribute to the continental shortening, although other parameters such as the subduction of passive ridges, the trench-parallel width of the slab, and eventually climate, may also influence the magnitude and the locus of shortening. The building of the Cordillera, indeed, occurred during several phases that are not everywhere coeval, and whose occurrence may partly result from changes in the kinematics of the plates. We present both analogue models (Guillaume et al., 2018) and 2D numerical experiments (Cerpa et al., submitted) simulating the subduction of an oceanic plate beneath an overriding continent advancing towards the trench at variable velocities. Analogue and numerical models confirm that the larger the upper plate trenchward velocity, the smaller the dip of the slab. Following a change in overriding plate velocity, slab dip evolves during a period, called the adjustment-time, to reach a state in equilibrium with the new boundary conditions. Models suggest that the transient adjustment-time of the slab geometry may last between ~13 and ~30 Myrs, meaning that the Andean subduction zone is not in steady-state, as most of the subduction zones worldwide. Models also show that the upper plate tectonic regime depends on its trenchward velocity. They suggest however that variations in overriding plate velocity may have a larger impact on its tectonic regime. When the trenchward motion of the overriding plate increases, an extra compressive force maintains as long as the slab geometry has not been adjusted to the new kinematic conditions. Conversely, overriding plate deceleration could trigger extension. We discuss the implications of these results on the evolution of the Andean Cordillera. Cerpa, N., B. Guillaume and J. Martinod, The interplay between overriding plate kinematics, slab dip and tectonics, Geophys. J. Int., submitted, 2018. Guillaume, B., S. Hertgen, J. Martinod and N. Cerpa, Slab dip, surface tectonics: How and when do they change following an acceleration/slow down of the overriding plate? Tectonophysics, 726, 110-120, 2018.