New geophysical data have revealed a large number of narrow and deep depressions in the ice sheet bed in various areas of Antarctica with depths of up to 3500 m below sea level (Denman Depression). These depressions have all the features of Cenozoic rifting – steep sides, the greatest depths on land, strong negative gravity anomalies in free air (–100 mGal and less) and high heat flow. The continuation of rifting after the glaciation of Antarctica with almost complete cessation of sedimentation under the ice explains the great depth and steep sides of the depressions with increased heat flow and mass deficit. Important features of the coastal depressions of the ice bed are their retrograde slopes, characteristic only of Antarctica. The subglacial relief of the basins on the approach to the continental coast sharply flattens out, which indicates sedimentation in the transition zone during periods of ice melting and subsequent marine regressions-transgressions in the Late Cenozoic. Increased heat flow can lead to melting of the glacier base and promote their accelerated sliding from the bedrock into the ocean. Another factor affecting the rate of glacier sliding into the ocean is the friction force with the bedrock. The presence of soft young sediments reduces friction and promotes the sliding of ice sheets into the ocean under the influence of gravity. Fast-moving ice sheets in Antarctica are mainly confined to areas of rift basins. Acceleration of glacier runoff along retrograde slopes into the ocean has a positive feedback and creates a potential hazard of global sea level rise. The geodynamic mechanism responsible for the Cenozoic activation of Antarctic rift zones is due to the action of local upper mantle plumes beneath Antarctica during and after the breakup of Gondwana. Further reactivation of extension along weakened zones in the lithosphere is associated with the general acceleration of global mantle convection that began in the Miocene. Numerical three-dimensional geodynamic models of the formation of the Transantarctic Mountains and the uplift of the Gamburtsev intraplate orogen in the Cenozoic are proposed.