After the onset of plate collision in the Alps, at 32-34 Ma, the deep structure of the orogen is inferred to have changed dramatically: European plate break-offs in various places of the Alpine arc, as well as a possible reversal of subduction polarity in the eastern Alps have been proposed. We review different high-resolution tomographic studies of the upper mantle and combine shear-and body-wave models to assess the most reliable geometries of the slabs. Several hypotheses for the tectonic evolution are presented and tested against the tomographic model interpretations and constraints from geologic and geodetic observations. We favor the interpretation of a recent European slab break-off under the western Alps. In the eastern Alps, we review three published scenarios for the subduction structure and propose a fourth one to reconcile the results from tomography and geology. We suggest that the fast slab anomalies are mainly due to European subduction; Adriatic subduction plays no or only a minor role along the Tauern window sections, possibly increasing towards the Dinarides. The apparent northward dip of the slab under the eastern Alps may be caused by imaging a combination of Adriatic slab, from the Dinaric subduction system, and a deeper lying European one, as well as by an overturned, retreating European slab.