Despite great advances in understanding of the earth’s climate, our estimate of the global temperature rise due to a doubling of atmospheric CO₂ has not greatly changed in a hundred years, and the estimate of the uncertainty on that number has actually increased. This is because while the basic mechanism of greenhouse-gas forcing of climate is well understood, the multiple, mostly positive, feedback loops that amplify this effect are not. The combined effect of many of these feedbacks can be seen in the record of past climate, and analysis of these suggests that our present models tend to under-predict the eventual, equilibrium climate change due to a given increase in atmospheric CO₂. In the foreseeable future (next 20 years) climate modelling research will probably not materially decrease the uncertainty on predictions for the climate of 2100. The uncertainty will only start to decrease as we actually observe what happens to the climate. The best use of climate models at present is via ensembles of predictions that give a probabilistic description of the range of uncertainty involved in future climate. Recent studies suggest a skewed probability distribution, with a tail stretching out to high climate sensitivities. Combined with estimates of the likely economic impact of climate change, this strongly suggests that research should be concentrated on trying to reduce the uncertainty represented by this tail of low probability, but high impact, scenarios.