Accurate models of past Antarctic ice sheet behaviour require realistic reconstructions of the evolution of bedrock topography. However, other than a preliminary attempt to reconstruct Antarctic topography at the Eocene–Oligocene boundary, the long-term evolution of Antarctica's subglacial topography throughout its glacial history has not previously been quantified. Here, we derive new reconstructions of Antarctic topography for four key time slices in Antarctica's climate and glacial history: the Eocene–Oligocene boundary (ca. 34 Ma), the Oligocene–Miocene boundary (ca. 23 Ma), the mid-Miocene climate transition (ca. 14 Ma), and the mid-Pliocene warm period (ca. 3.5 Ma). To reconstruct past topography, we consider a series of processes including ice sheet loading, volcanism, thermal subsidence, horizontal plate motion, erosion, sedimentation and flexural isostatic adjustment, and validate our models where possible using onshore and offshore geological constraints. Our reconstructions show that the land area of Antarctica situated above sea level was ~25% larger at the Eocene–Oligocene boundary than at the present-day. Offshore sediment records and terrestrial constraints indicate that the incision of deep subglacial topographic troughs around the margin of East Antarctica occurred predominantly in the Oligocene and early Miocene, whereas in West Antarctica erosion and sedimentation rates accelerated after the mid-Miocene. Changes to the topography after the mid-Pliocene were comparatively minor. Our new palaeotopography reconstructions provide a critical boundary condition for models seeking to understand past behaviour of the Antarctic Ice Sheet, and have implications for estimating changes in global ice volume, temperature, and sea level across major Cenozoic climate transitions.