This Introduction addresses questions of migration, history, and memory in the context of recent changes in public discourses on immigrant integration in Europe, focusing on how history is used to make claims about the inclusion of some and the exclusion of others. We highlight how these debates are often framed in a nostalgic tone that sustains categorizations and classifications of the population in terms of 'natives', who are allegedly historically rooted, and non-natives, lacking historical roots. To shed light on this process, we put forward the notion of historical repertoires to refer to ways that views of history are used to evaluate and justify the present. We lay out three possible components of these repertoires, showing their utility in analysing the debates discussed in the six European case studies in this issue (Germany, Hungary, the Netherlands, the United Kingdom, France, and Greece). We also consider some parallels with the United States in how the history of immigration is remembered and used in public debates and political discourse.