Recent years have seen much attention, media and political, given to the movement of people. This is especially the case in terms of the extraordinary movements precipitated by war, famine, and the ravages of global warming, that have produced refugees in seemingly greater numbers. They have also produced hostile responses with the building of walls and fences, the denial of aid and solidarity, and changes to citizenship laws which have often turned citizens into migrants to be policed even more harshly. Global crises related to the movement of populations recur with relative regularity and yet each is presented as unprecedented, reproducing the idea of crisis in the process. This occurs not just in media representations and political debate, but also in academic accounts of migration which often use similar framings in their analyses. In this talk, I argue for the need to take colonial histories seriously in our understandings of contemporary migration. The population movements from Europe to the New World and beyond coalesced, over four centuries, into a phenomenon that was markedly different from these other quotidian movements and encounters. This is because European movement was linked to colonial settlement which was central to the displacement, dispossession, and elimination of populations across the globe. It was also central to the creation of the global inequalities and injustices that mark the worlds we share in common and that are the basis of contemporary movements of peoples. Without understanding the histories that produced these inequalities we are unlikely to understand contemporary movements.