Five major themes are often addressed in the discourse of mobility in science: The definition and classification of the persons in mind (scholars, academics, researchers, etc,), the frequency and the configuration of mobility, the role mobility and migration plays for the individuals, the role they play for institutions (universities, research institutes, enterprises, etc.), and finally the relevance of mobility and migration for the overall international activities within higher education and research in a ‘globalized world’. This article summarizes the concepts and findings presented as regards these themes in all the article of this journal issue. The discourse both on concepts and findings suggests that mobility and migration is often viewed in isolation rather than in a wider context of features of internationalisation. Moreover, attention often focuses on mobility and migration at the apex of the prestige and quality pyramid notably in the countries most strongly involved; differences by country, sector and position in the reputational hierarchy would be viewed as more relevant, if European policies strived for a balance between market developments and cohesion across Europe and for keeping inequalities between European countries within limits.