Most of the Greenland and Antarctic ice sheets are covered with firn — the transitional material between snow and glacial ice. Firn is vital for understanding ice-sheet mass balance and hydrology, and palaeoclimate. In this Review, we synthesize knowledge of firn, including its formation, observation, modelling and relevance to ice sheets. The refreezing of meltwater in the pore space of firn currently prevents 50% of meltwater in Greenland from running off into the ocean and protects Antarctic ice shelves from catastrophic collapse. Continued atmospheric warming could inhibit future protection against mass loss. For example, warming in Greenland has already contributed to a 5% reduction in firn pore space since 1980. All projections of future firn change suggest that surface meltwater will have an increasing impact on firn, with melt occurring tens to hundreds of kilometres further inland in Greenland, and more extensively on Antarctic ice shelves. Although progress in observation and modelling techniques has led to a well-established understanding of firn, the large uncertainties associated with meltwater percolation processes (refreezing, ice-layer formation and storage) must be reduced further. A tighter integration of modelling components (firn, atmosphere and ice-sheet models) will also be needed to better simulate ice-sheet responses to anthropogenic warming and to quantify future sea-level rise.