Recent deep seismic-reflection profiling has shown a diversity of structure associated with the lowermost crust. A typically unreflective mantle is overlain by reflections in the lower crust. Many of these are subhorizontal and are attributed to lithological layering or to shearing in which the horizontal fabric is generated by ductile lateral flow, exemplified by pure shear. The subhorizontal reflectors in places are cut by dipping reflectors commonly interpreted as inclined shear zones, which are representative of simple shear. The prevalence of simple over pure shear in deep lithosphere deformation is discussed--it has important consequences for the symmetry of development of sedimentary basins, and for their thermal history. Basins around the margins of the North tlantic show a diverse set of relationships with the underlying deep crust. Despite the evidence of abundant simple shear, crustal thinning directly below most basins fits models of pure-shear deformation of the deep crust. The apparent conflict can be resolved by recognizing that large-scale pure shear can be produced by an appropriate balance of oppositely directed smaller scale simple shears. Rift basins commonly show asymmetry related to pre-existing deep crustal fabrics. Saucer-shaped basins may result from thermal subsidence after differential stretching and transformation of upper crust into characteristic lower crust by sill intrusion.