Apatite and zircon fission track (FT) thermochronology, as well as regional geologic data, are used to assess the tectonic and climatic mechanisms responsible for exhumation of Svalbard during the last 70 million years. Four stratigraphic profiles in the Paleogene Central basin spanning ~0.6--1.1 km vertical relief yield apatite FT ages ranging from 28.3¿2.3 Ma to 41.8¿3.7 Ma, with a mean age of ~36 Ma and no apparent vertical trend. Apatite ages from the Paleogene Forlandsundet and Kongsfjorden basins and the Late Cretaceous-Tertiary Svalbard Orogen range from 26.8¿3.7 to 55.7¿4.7 Ma, with Kongsfjorden data suggesting cooling earlier than the Central basin. Although 10 detrital zircon samples were analyzed from both the Forlandsundet and Central basins, only one sample (from the basal Paleogene deposits in the northwesternmost Forlandsundet basin) had a reset age of 42.4¿1.8 Ma. Nonreset detrital zircons elsewhere retain Caledonian and Proterozoic detrital ages. Thermal-history models derived from apatite track-length distributions of six Central and Kongsfjorden basin samples indicate a strikingly consistent five-phase thermal history. Initial uplift of sediment sources to the north and west is recorded as a 70--50 Ma cooling signature. Following deposition from 63 to 49 Ma, the samples were heated until ~35 Ma, probably as the result of continued sediment burial. This basin filling coincided with a dextral continental transform connecting spreading ridges in the Arctic and Norwegian-Greenland oceanic basins. The thermal models are consistent with ~40¿--50 ¿C of cooling from ~35 to 25 Ma. This cooling, which is consistent with deposition patterns both onshore and offshore, appears to be the result of rift-related uplift and erosion as the Atlantic spreading ridge propagated northward to separate Greenland from Svalbard. Track-length models are consistent with thermal stasis from ~25 Ma to 5 Ma, despite sedimentation in offshore Miocene basins suggesting that continued erosion was occurring. We suggest that an increase in the geothermal gradient (by the Yermak Hot Spot and associated onshore volcanism) offset cooling expected at this time as the result of continued erosion. A final rapid post-5 Ma cooling phase of ~70 ¿C is attributed to ~2.1 km of erosion in response to intensified glacial denudation. Pliocene-Holocene cooling, which occurred despite a persistently elevated geothermal gradient, is consistent with offshore evidence for first ice cover in the Norwegian-Greenland Sea at 5.5 Ma and a substantially increased sediment flux to continental-slope basins from 5.0 to 0.44 Ma. ¿ 1998 American Geophysical Union