Ongoing climate change is assumed to be exceptional because of its unprecedented velocity. However, new geophysical research suggests that dramatic climatic changes during the Late Pleistocene occurred extremely rapid, over just a few years. These abrupt climatic changes may have been even faster than contemporary ones, but relatively few continent-wide extinctions of species have been documented for these periods. This raises questions about the ability of extant species to adapt to ongoing climate change. We propose that the advances in geophysical research challenge current views about species' ability to cope with climate change, and that lessons must be learned for modelling future impacts of climate change on species.