This article aims to discuss the supervision process for master and doctoral students in graduate courses. Considering the literature on the subject, we defined three educational responsibilities to be developed by the supervisor for the student (researcher, teacher and professional), and we delimited six dimensions for consideration (intellectual, social, contextual, emotional, moral and political). Based on these delimitations, we proposed a set of features and activities for the education of masters and doctoral students. Concluding, we made some comments and recommendations on practices to be implemented and to be avoided during the supervision process.