The geology beneath Thwaites Glacier, the Antarctic glacial catchment most vulnerable to climate change, is unknown. Thwaites Glacier lies within the West Antarctic Rift System, but details of the subglacial geology relevant to glacial flow, including sediment availability, underlying lithology, and heat flux, are lacking. We present the first sketch map of the subglacial geology of Thwaites Glacier, interpreted from maps of airborne gravity, magnetic and radar data, supported by 2D models and 3D inversion of subsurface properties, and the regional geological context. A zone of Cretaceous mafic magmatism extending ~200 km inland from the coast is interpreted, while sedimentary basins are restricted to a region 150 to 200 km inboard of the coast, underlying just 20% of the catchment. Several granitic subglacial highlands are identified, forming long-lived topographic highs. Our geological interpretation places constraints on the basal properties of Thwaites Glacier, laying the foundation for both improved predictions of ice sheet change and studies of West Antarctic tectonics.