Detailed and reliable understanding of past climate change is a key ingredient in unravelling how climate has infl uenced life on earth and will continue to do so in the future. Palaeoclimatology and climate modelling have both made rapid strides over the past decades, and there has been fruitful two-way interaction between the two fi elds. Th e application of climate models to palaeoclimates has proved useful both in interpreting palaeoclimate proxy data and in testing the robustness and generality of climate models. Here, we give an overview of the current state of climate modelling and review recent progress in understanding deep-time climate change, with emphasis on problems where climate models have played a salient role. By suitably adjusting the concentration of atmospheric greenhouse gases, climate models can be made to replicate many key climatic transitions in the earth's history. However, important discrepancies remain between modelled climates and proxy reconstructions, particularly on the warm end of the spectrum.