A considerable body of evidence indicates that many of the extensional sedimentary basins in the vicinity of the British Isles underwent permanent exhumation during the Tertiary. The most dramatic indicator of this process is the present-day absence of as much as 4 km of anticipated postrift thermal subsidence in basins just north and west of Scotland. Any explanation of this observation must take into account the fact that the entire region has very small,-long-wavelength, free-air gravity anomalies. This important constraint implies either that the crust has been thickened or that low-density material has been added to or formed from the lithosphere and rules out models that invoke flexural effects arising from the opening of the North Atlantic. Tertiary epeirogeny is often attributed to compression that is assumed to be related in a general sense to Alpine mountain building. However, to remove ∼3 km of sedi- mentary rock from a basin ∼100 km wide requires >15 km of shortening. Minor Tertiary compression is observed all over the continental shelf, but nowhere is it sufficient to account for the required amount of uplift and erosion. In addition, exhumation dramatically increases from south to north, whereas the observed compression decreases markedly in the same direction. At the beginning of the Tertiary, rifting associated with the initiation of the Iceland plume generated substantial volumes of melt. Inversion of rare-earth- element concentrations of MgOrich igneous rocks suggests that a minimum of ∼5 km of melt was produced beneath at least part of the continental shelf. We infer that much of this melt remains trapped within the lithosphere, presumably close to the Moho, which acted as a density filter. Such underplating will generate rapid uplift.