Since the creation of the Erasmus program (an acronym for the European Action Scheme for the Mobility of University Students) in 1987, the form and scope of student exchanges within the European Union have changed significantly. Until recently, only the higher education level and its educational community was concerned with the institutionalization of mobility. Today, Erasmus+ encompasses other types of exchanges and reaches out more broadly to European youth. This article is a synthesis of the evolution of European educational policies and public actions around mobility. We will also address the question of the evolution of the discourse that accompanies these policies, notably concerning the existence of an Erasmus "generation", and that of the trajectories that this program allows, according to the segments and levels of education concerned, from higher education to compulsory education.