A dominant characteristic of the available simulations of past sea ice changes is the strong link between the model results for modern and past climates. Nearly all the models have similar extent for pre-industrial conditions and for the mid-Holocene. The models with the largest extent at Last Glacial Maximum (LGM) are also characterized by large pre-industrial values. As a consequence, the causes of model biases and of the spread of model responses identified for present-day conditions appear relevant when simulating the past sea ice changes. Nevertheless, the models that display a relatively realistic sea-ice cover for present-day conditions often display contrasted response for some past periods. The difference appears particularly large for the LGM in the Southern Ocean and for the summer ice extent in the Arctic for the early Holocene (and to a smaller extent for the mid-Holocene). Those periods are thus key ones to evaluate model behaviour and model physics in conditions different from those of the last decades. Paleoclimate modelling is also an invaluable tool to test hypotheses that could explain the signal recorded by proxies and thus to improve our understanding of climate dynamics. Model analyses have been focused on specific processes, such as the role of atmospheric and ocean heat transport in sea ice changes or the relative magnitude of the model response to different forcings. The studies devoted to the early Holocene provide an interesting example in this framework as both radiative forcing and freshwater discharge from the ice sheets were very different compared to now. This is thus a good target to identify the dominant processes ruling the system behaviour and to evaluate the way models represent them. © 2013 Elsevier Ltd.