The Alpine Pyrenean-Cantabrian orogen developed along the plate boundary between Iberia and Europe, involving the inversion of Mesozoic hyperextended basins along the southern Biscay margin. Thus, this margin represents a natural laboratory to analyze the control of structural rift inheritance on the compressional reactivation of a continental margin. With the aim to identify former rift domains and investigate their role during the subsequent compression, we performed a structural analysis of the central and western North Iberian margin, based on the interpretation of seismic reflection profiles and local constraints from drill-hole data. Seismic interpretations and published seismic velocity models enabled the development of crustal thickness maps that helped to constrain further the offshore and onshore segmentation. Based on all these constraints, we present a rift domain map across the central and western North Iberian margin, as far as the adjacent western Cantabrian Mountains. Furthermore, we provide a first-order description of the margin segmentation resulting from its polyphase tectonic evolution. The most striking result is the presence of a hyperthinned domain (e.g., Asturian Basin) along the central continental platform that is bounded to the north by the Le Danois High, interpreted as a rift-related continental block separating two distinctive hyperextended domains. From the analysis of the rift domain map and the distribution of reactivation structures, we conclude that the landward limit of the necking domain and the hyperextended domains, respectively, guide and localize the compressional overprint. The Le Danois block acted as a local buttress, conditioning the inversion of the Asturian Basin.