International migration regimes refer to the way states interact when there are flows or pressures for flows of people with the prospect of lasting settlement across their borders. States generally enforce border checks, recognise only a limited right of residence, reduce social security rights outside the country of employment and deny civic rights for migrants. In Europe in the late 1940s, states routinely responded to migration flows with such cumbersome and arbitrary administrative practices. Today, in contrast, the regime of migration between the member states of the European Union (EU) displays openness. Migrants’ social security rights are exportable, and they benefit from civic rights. Deep closure towards low-skilled migration from outside Europe also characterises this regime, however. During the post-war decades, change has defied continuity, and today’s liberal migration regime has achieved depth, width and longevity, making it without equivalent in modern history.