At its simplest, migration refers to the movement of people and their temporary or permanent geographical relocation. People have always been on the move and they have moved over great distances. In this article I set out a brief historical understanding of migration, and then focus on Europe and, finally, current dilemmas of European migration policy. In an era of climate change, war and uneven development, the pressures of migration have grown and could soon create an ever greater avalanche of movement. States act in a paradoxical way. On the one hand, they recognise the nature of the migration crisis and the necessity to broaden the definition of those who need urgent assistance. On the other hand, most host countries act on increasingly narrow definitions of those who warrant assistance and perhaps resettlement. This dilemma is examined and tentative steps are set down to show how it might be resolved.