Characterizing glaciotectonic deformation, glacial erosion and sedimentation, and basal hydrologic conditions of ice sheets is vital for selecting sites for nuclear waste repositories at high latitudes. Glaciotectonic deformation is enhanced by excess pore pressures that commonly persist near ice sheet margins. Depths of such deformation can extend locally to a few tens of meters, with depths up to approximately 300 m in exceptional cases. Rates of glacial erosion are highly variable (0.05–15 mm a−1), but rates <1 mm a−1 are expected in tectonically quiescent regions. Total erosion probably not exceeding several tens of meters is expected during a glacial cycle, although locally erosion could be greater. Consolidation of glacial sediments that is less than expected from independent estimates of glacier thickness indicates that heads at the bases of past ice sheets were usually within 30% of the floatation value. This conclusion is reinforced by direct measurements of water pressure beneath portions of the West Antarctic ice sheet, which indicate average heads <7 m below floatation. Landforms of the Laurentide and Scandinavian ice sheets and recent observations in Greenland indicate that high seasonal discharges of surface water are conducted to the bed, despite thick ice at subfreezing temperatures. Therefore, in models of subglacial groundwater flow used to assess sites for nuclear waste repositories, a flux upper boundary condition based on water input from only basal melting will be far more uncertain than applying a hydraulic head at the upper boundary set equal to a large fraction of the floatation value.