Anthropogenic climate change will continue long after anthropogenic CO2 emissions cease. Atmospheric CO2, global warming and ocean circulation will approach equilibrium on the millennial timescale, whereas thermal expansion of the ocean, ice sheet melt and their contributions to sea level rise are unlikely to be complete. Atmospheric CO2 in year 3000 depends non-linearly on the total amount Of CO2 emitted and is very likely to exceed the present level of similar to 380 ppmv. CO2 is doubled for similar to 2500 GtC emitted, quadrupled if all similar to 5000 GtC of conventional fossil fuel resources are emitted, and increases by a factor of similar to 32 if a further 20,000 GtC of exotic fossil fuel resources are emitted. Global warming in year 3000 will also depend on climate sensitivity to doubling CO2, which is most probably similar to 3 degrees C but highly uncertain. Thermal expansion will contribute 0.5-2 m to millennial sea level rise for each doubling of CO2. The Greenland ice sheet could melt completely within the millennium under > 8 x CO2, adding a further similar to 7 m to sea level. The rate of melt depends on the magnitude of forcing above a regional warming threshold of 1-3 degrees C. The West Antarctic ice sheet could be threatened by 4-10 degrees C local warming, and its potential contribution to millennial sea level rise exceeds current maximum estimates of similar to 1 m. The fate of the ocean thermohaline circulation may depend on the rate as well as the magnitude of forcing.