It is often assumed within much of the academic literature and by many of those working in higher education that universities across Europe are homogenising, converging around an Anglo-American model as a result of neo-liberal pressures and the aim of creating a single European Higher Education Area. However, drawing on an analysis of 92 policy documents from six different European countries, this article demonstrates that enduring differences remain -- at least in so far as constructions of students are concerned. While European policy may assume that higher education students can move unproblematically across national borders, as part of the Erasmus mobility scheme, for example, the article shows that understandings of 'the student' differ in significant ways both across countries and, to some extent, within them. This has implications for both European policy and academic theorisation.