We present observations that demonstrate that the elevated passive margins around the North Atlantic were formed by episodic, post-rift uplift movements that are manifest in the high-lying peneplains that characterize the coastal mountains, in the unconformities in the adjacent sedimentary basins and in accelerated subsidence in the basin centres. Results from West Greenland show that subsidence of the rifted margin took place for c. 25 Myr after rifting and breakup in the Paleocene, as predicted by classical rift theory, but that this development was reversed by a series of uplift movements (starting at c. 35, 10 and 5 Ma) that remain unexplained. East Greenland and Scandinavia seem to have had a similar evolution of post-rift subsidence followed by uplift starting at c. 35 Ma. There was no notable fall in sea-level at this time, so the subsiding basins must have been inverted by tectonic forces. We speculate that the forces causing this phase were related to the plate boundary reorganization in the North Atlantic around Chron 13 time. One feature that these areas have in common is that uplift took place along the edges of cratons where the thickness of the crust and lithosphere changes substantially over a short distance. It may be that the lateral contrasts in the properties of the stretched and unstretched lithosphere make the margins of the cratons unstable long after rifting. These vertical movements have profound influence on hydrocarbon systems, not only in frontier areas such as West and East Greenland, where Mesozoic basins are deeply truncated and exposed onshore, but also for the understanding of near-shore hydrocarbon deposits in mature areas such as the North Sea Basin, where low-angular unconformities may represent episodes of deposition and removal of significant sedimentary sections.