How much can we trust model-based projections of future anthropogenic climate change? This review attempts to give an overview of this important but difficult topic by using three main lines of evidence: the skill of models in simulating present-day climate, intermodel agreement on future climate changes, and the ability of models to simulate climate changes that have already occurred. A comparison of simulated and observed present-day climates shows good agreement for many basic variables, particularly at large horizontal scales, and a tendency for biases to vary in sign between different models, but there is a risk that these features might be partly a result of tuning. Overall, the connection between model skill in simulating present-day climate and the skill in simulating future climate changes is poorly known. An intercomparison of future climate changes between models shows a better agreement for changes in temperature than that for precipitation and sea level pressure, but some aspects of change in the latter two variables are also quite consistent between models. A comparison of simulations with observed climate changes is, in principle, a good test for the models, but there are several complications. Nonetheless, models have skilfully simulated many large-scale aspects of observed climate changes, including but not limited to the evolution of the global mean surface air temperature in the 20th century. Furthermore, although there is no detailed agreement between the simulated and observed geographical patterns of change, the grid box scale temperature, precipitation and pressure changes observed during the past half-century generally fall within the range of model results. Considering the difficulties associated with other sources of information, the variation of climate changes between different models is probably the most meaningful measure of uncertainty that is presently available. In general, however, this measure is more likely to underestimate than overestimate the actual uncertainty.