The Andean margin is the plate-tectonic paradigm for long-lived, continuous subduction, yet its geology since the late Mesozoic era (the past 100 million years or so) has been far from steady state. The episodic deformation and magmatism have been attributed to cyclic changes in the dip angle of the subducting slab, slab break-off and the penetration of the slab into the lower mantle; the role of plate tectonics remains unclear, owing to the extensive subduction of the NazcaFarallon plate (which has resulted in more than 5,500 kilometres of lithosphere being lost to the mantle). Here, using tomographic data, we recreate the plate-tectonic geometry of the subducted Nazca slab, which enables us to reconstruct Andean plate tectonics since the late Mesozoic. Our model suggests that the current phase of Nazca subduction began at the northern Andes (5 degrees S) during the late Cretaceous period (around 80 million years ago) and propagated southwards, reaching the southern Andes (40 degrees S) by the early Cenozoic era (around 55 million year ago). Thus, contrary to the current paradigm, Nazca subduction has not been fully continuous since the Mesozoic but instead included episodic divergent phases. In addition, we find that foredeep sedimentation and the initiation of Andean compression are both linked to interactions between the Nazca slab and the lower mantle, consistent with previous modelling.