The rate of global mean sea level rise (GMSLR) has accelerated during the last two centuries, from the order of magnitude of 0.1 mm/yr during the late Holocene, to about 1.5 mm/yr for 1901-1990. Thermal expansion of the ocean and glacier mass loss are probably the dominant contributors. During the last couple of decades the rate of rise has been larger, at around about 3 mm/yr, because of increased radiative forcing of climate change due to greenhouse gases, and increased ice-sheet outflow induced by warming of the immediately adjacent ocean. Up to the middle of the 21st century, projections of GMSLR under various scenarios of greenhouse-gas emissions have a small spread, because of the time-integrating characteristic of GMSLR. However by 2100 the rate of GMSLR for a scenario of high emissions could approach the average rates that occurred during the last deglaciation, whereas for a scenario with strong mitigation of emissions it could stabilise at rates similar to those of the early 21st century. The largest expected contribution to GMSLR in the 21st century is thermal expansion, but the greatest uncertainty in projections comes from ice-sheet dynamical change. Climate models also exhibit substantial disagreement in the geographical pattern of sea level change due to ocean density and circulation change. GMSLR will continue for many subsequent centuries, because of the long timescales of ice-sheet change and deep-ocean warming. Potentially it could amount eventually to many metres, and could be partly irreversible.