How quickly greenhouse-gas emissions need to be reduced in order to avoid what has been termed dangerous climate change is of fundamental importance. Two papers in this issue tackle the question from different standpoints, yet come to broadly similar conclusions. Meinshausen et al. relate the cumulative emission of greenhouse gasses by 2050 to the probability of exceeding the 2 °C of global warming above pre-industrial temperatures adopted by more than 100 countries as the threshold of dangerous climate change. They find that only about a third of economically recoverable oil, gas and coal reserves can be burned if global warming of 2 °C is to be avoided by 2100, an amount of fossil fuel that would be burned by 2029 if consumption remains at today's levels. Allen et al. use a combined climate and carbon cycle model to produce simulations spanning a range of climate futures consistent with the changes already observed. The 500 billionth tonne of anthropogenic carbon since 1750 was recently released into the atmosphere, and Allen et al. find that releasing a trillion tonnes of carbon in total is likely to cause a peak warming exceeding the 'acceptable' 2 °C temperature increase. Every tonne released thereafter increases the committed maximum warming in a predictable way, regardless of when it is released. Any effective climate mitigation regime must therefore achieve a cap on cumulative carbon dioxide emissions — one trillion tonnes would be a possible though optimistic target. In News and Views, Gavin Schmidt and David Archer consider these papers and other recent work focusing on establishing achievable emissions targets.