Storing ice volumes of more than 65 meters sea-level equivalent, the ice sheets on Greenland and Antarctica are by far the largest potential source of future sea-level rise. Their long-term stability thus determines the fate of our coastal cities and cultural heritage sites. While massive in size, the ice sheets also belong to the most vulnerable parts of the Earth system: feedbacks between ice, atmosphere and ocean give rise to non-linearities in their response to progressing global warming. Once a critical temperature threshold is crossed, this could lead to self-sustained and potentially irreversible ice loss from drainage basins in Greenland and Antarctica. In this lecture, we will review the processes behind these dynamic instabilities, discuss the potential of crossing ice-sheet tipping points in the future, and explore the resulting impacts on sea-level rise and our global climate – not just for this century, but for the next millennia and beyond.