The great ice sheets covering Antarctica and Greenland were, traditionally, believed to take thousands of years to respond to external forcing. Recent observations suggest, however, that major changes in the dynamics of parts of the ice sheets are taking place over timescales of years. These changes were not predicted by numerical models, and the underlying cause(s) remains uncertain. It has been suggested that regional oceanic and/or atmospheric warming are responsible but separating the influence and importance of these two forcings has not been possible. In most cases, the role of atmospheric versus oceanic control remains uncertain. Here, we review the observations of rapid change and discuss the possible mechanisms, in the light of advances in numerical modelling and our understanding of the processes that may be responsible.