The ice sheets of Greenland and Antarctica are losing ice at accelerating rates, much of which is a response to oceanic forcing, especially of the floating ice shelves. Recent observations establish a clear correspondence between the increased delivery of oceanic heat to the ice-sheet margin and increased ice loss. In Antarctica, most of these processes are reasonably well understood but have not been rigorously quantified. In Greenland, an understanding of the processes by which warmer ocean temperatures drive the observed retreat remains elusive. Experiments designed to identify the relevant processes are confounded by the logistical difficulties of instrumenting ice-choked fjords with actively calving glaciers. For both ice sheets, multiple challenges remain before the fully coupled ice-ocean-atmosphere models needed for rigorous sea-level projection are available.