Structurally, the North Atlantic margins are characterized by Late Cretaceous-Early Tertiary extension, developing predominantly rifted segments south of the Greenland-Senja Fracture Zone, and by oblique extension and wrenching leading to large sheared margin segments further north. The rifted segments document an intense, transient volcanic phase during break-up, emplacing huge extrusive constructions on the outer margin. Commercial exploration has mostly been landward of the shelf edge, but lately there is increased interest in the deep water basins on the outer margins and in the perennially sea-ice-covered shelf off Greenland. Evaluation of these areas requires an understanding of the processes and events prior, during and after the Paleocene-Eocene opening of the North Atlantic. Although the margin is a Cenozoic feature, its segmentation and evolution are governed by the pre-opening history, particularly the Late Jurassic-Early Cretaceous tectonic episode which resulted in large Cretaceous sedimentary basins. Moreover, the first few multi-channel seismic profiles from the NE Greenland inner shelf north of 79°N show a deep Permo-Carboniferous rift basin. The similarity of tectono-magmatic features off NE Greenland and Norway shows the value that conjugate margin studies provide in understanding volcanic margin formation. The events at break-up affected both the subsidence and thermal histories of the marginal basins and were associated with crustal uplift and erosion of the rift region, intrusive activity within the adjacent Mesozoic basins and lava flows spilling onto large areas of the pre-opening crust. The transient magmatism/volcanism had important environmental implications. After break-up, the margin experienced thermal subsidence and little structural deformation, but the extrusive complexes controlled the Paleogene sediment deposition.