A regional three-dimensional model has been constructed for the lithospheric structure of the NE Atlantic margin. Starting from the known bathymetry and an initial sediment thickness estimate and making allowance for thermal effects, the geometry of the crystalline crust was predicted using isostatic and flexural principles. Optimization methods were then used to modify the base sediment and Moho interfaces to improve the fit between observed and calculated gravity anomalies. The method provides new insights into basin morphology and into variations in the thickness of both crystalline continental crust and igneous oceanic crust. When combined with imaging of the gravity and magnetic fields, the model highlights the importance of broadly NW-trending lineaments on the development of post-Caledonian basin architecture. In some cases these lineaments are interpreted as pre-Caledonian structures that were reactivated as transfer zones during phases of Mesozoic extension. Some of the lineaments appear to have influenced the early evolution of the oceanic crust by providing the precursors to transform offsets and possibly also by affecting the pattern of asthenospheric flow. The crustal thickening of the Faroe–Iceland Ridge is clearly imaged and its geometry is interpreted to reflect temporal variations in the enhanced oceanic crustal production rate responsible for this feature, including a Late Eocene minimum which can be correlated with plate reorganization in the north Atlantic region. There is some evidence of Cenozoic deformation linked to transpressive reactivation of the lineaments. However, a deflection in the axis of the North Hatton Anticline across the NW-trending Anton Dohrn lineament is more likely to have been inherited from an offset in an underlying, reactivated basement structure than to have resulted from strike-slip movements at the time of folding.