The secondary-tertiary transition has been studied in a great amount of research in mathematics education, adopting different focuses and theoretical approaches. I present here how these focuses led the authors to identify and study different students' difficulties and to develop different means of didactical action. Individual, social, but also institutional phenomena are considered with different perspectives. Each perspective yields a particular view of transition. The association and comparison of these views makes it possible to build an organized outline of this complex object, combining several kinds of ruptures and long-term evolutions.