Rapid, or abrupt, climate change is regarded as a change in the climate system to a new state following the crossing of a threshold. It generally occurs at a rate exceeding that of the change in the underlying cause. Episodes of rapid climate change abound in the recent geological past (defined here as the interval between the last glacial maximum, dated to approximately 20,000 years ago, and the present). Rapid climate changes are known to have occurred over time periods equal to or even less than a human lifespan: moreover, their effects on the global system are sufficiently large to have had significant societal impacts. The potential for similar events to occur in the future provides an important impetus for investigating the nature and causes of rapid climate change. This paper provides a brief overview of rapid climate change and an introduction to this special issue, which presents results generated by the palaeoclimatic component of the UK Natural Environment Research Council’s rapid climate change programme, called RAPID. The papers in the special issue employ palaeoclimatic proxy data-sets obtained from marine, ice core and terrestrial archives to reconstruct rapid climate change during the last glacial cycle, its subsequent termination and the ensuing Holocene interglacial; some papers also report new attempts to match the palaeoclimate data to hypothesised causes through numerical modelling. The results confirm the importance of freshwater forcing in triggering changes in Atlantic meridional overturning circulation (MOC) and the close links between MOC and rapid climate change. While advancing our understanding of these linkages, the RAPID research has highlighted the need for further research in order to elucidate more specific details of the mechanisms involved.