This study provides 39 new thermochronometric analyses from the western part of the Greater Caucasus, a region in which existing data are extremely limited and of questionable quality. The new results are consistent with field studies that identify Triassic to Middle Jurassic (Cimmerian) and Oligo-Miocene (Alpine) orogenic erosional events. An inverse relationship between the fission track and depositional ages of Oligo-Miocene sedimentary samples also implies some degree of Eocene erosion of the Greater Caucasus and intermediate sediment storage. Cooling ages and field relationships within the core of the range, west of Mt Elbrus, require ~5 km of Permo-Triassic exhumation and restrict the overall amount of Cenozoic exhumation to ~2.5 km. Current exhumation rates are typically low, and do not support a Plio-Pleistocene increase in climate-driven denudation. High (~1 km Ma−1) rates of exhumation are restricted to the southern flank of the range in northwest Georgia. Despite a general lack of significant seismicity within the study region, this exhumation peak is close to the largest instrumentally recorded earthquake in the Caucasus (Ms = 7.0). This may suggest that exhumation is associated with the decoupling of the sedimentary succession from its crystalline basement in the southern part of the range and the inversion of the largely Jurassic fill of the Greater Caucasus basin. Rates of exhumation are compatible with this being driven by active shortening. Further sampling and analysis are required to provide a higher-resolution, low-temperature thermochronology of Alpine exhumation, to isolate the drivers for Palaeogene Dziruli Massif cooling and uplift, and to constrain better the extent of the current, localized phase of rapid exhumation.