CO2 released from combustion of fossil fuels equilibrates among the various carbon reservoirs of the atmosphere, the ocean, and the terrestrial biosphere on timescales of a few centuries. However, a sizeable fraction of the CO2 remains in the atmosphere, awaiting a return to the solid earth by much slower weathering processes and deposition of CaCO3. Common measures of the atmospheric lifetime of CO2, including the e-folding time scale, disregard the long tail. Its neglect in the calculation of global warming potentials leads many to underestimate the longevity of anthropogenic global warming. Here, we review the past literature on the atmospheric lifetime of fossil fuel CO2 and its impact on climate, and we present initial results from a model intercomparison project on this topic. The models agree that 20-35% of the CO2 remains in the atmosphere after equilibration with the ocean (2-20 centuries). Neutralization by CaCO3 draws the airborne fraction down further on timescales of 3 to 7 kyr.