Abstract. The structural styles and magnitudes of Alpine tectonic inversion are reviewed for the Atlantic margin of southwestern (SW) Iberia, a region known for its historical earthquakes, tsunamis and associated geohazards. Reprocessed, high-quality 2D seismic data provide new images of tectonic faults, which were mapped to a depth exceeding 10 km for the first time. A total of 26 of these faults comprise syn-rift structures accommodating vertical uplift and horizontal advection (shortening) during Alpine tectonics. At the regional scale, tectonic reactivation has been marked by (a) the exhumation of parts of the present-day continental shelf, (b) local folding and thrusting of strata at the foot of the continental slope, and (c) oversteepening of syn- and post-rift sequences near reactivated faults (e.g. “passive uplift”). This work proves, for the first time, that geometric coherence dominated the growth and linkage of the 26 offshore faults mapped in SW Iberia; therefore, they are prone to reactivate as a kinematically coherent fault network. They form 100–250 km long structures, the longest of which may generate earthquakes with a momentum magnitude (Mw) of 8.0. Tectonic inversion started in the Late Cretaceous, and its magnitude is greater close to where magmatic intrusions are identified. In contrast to previous models, this work postulates that regions in which Late Mesozoic magmatism was more intense comprise thickened, harder crust and form lateral buttresses to northwest–southeast compression. It shows these structural buttresses to have promoted the development of early stage fold-and-thrust belts – typical of convergent margins – in two distinct sectors.