Abstract We use the Bay of Biscay and Western Pyrenees as a natural laboratory to develop and apply an approach to characterize and identify distinctive rifted margin domains in offshore and onshore settings. The Bay of Biscay and Western Pyrenees offer access to seismically imaged, drilled and exposed parts of one and the same hyperextended rift system. Offshore, we use gravity inversion and flexural backstripping techniques combined with seismic interpretation to provide estimates of accommodation space, crustal thickness and lithosphere thinning. Onshore, we focus on key outcrops of the former rift domain to describe the nature of sediment and basement rocks, and of their interface. This qualitative and quantitative characterization provides diagnostic elements for the identification of five distinct structural domains at magma-poor rifted margins and their fossil analogues (proximal, necking, hyperthinned, exhumed mantle and oceanic domains). This new approach can be used to reconcile offshore and onshore observations, and to aid interpretation when only local observations are available. Onshore remnants can be placed in an offshore rifted-margin context, enabling the prediction of first-order crustal architecture. For the interpretation of offshore seismic reflection sections, geological insights into rift structures and basement nature can be suggested based on onshore analogies. Supplementary material: Sensitivity of backstripping results to flexural rigidity is available at http://www.geolsoc.org.uk/SUP18778 .