The massification and correlative extension of postgraduate university studies (master and doctoral degrees) have generated a disturbing individual and social problem related to increased drop-out rates. A certain number of postgraduate and PhD students and researchers leave their education, and this issue could be a larger problem for students in masters and doctoral programs than for registered students in undergraduate university studies. The phenomenon of persistence and non-persistence in doctoral studies is not new; several findings on this subject have been published since the early 1960’s in the United States and to a lesser extent in other countries. We now have extensive literature on this theme. Five major aspects related to drop-outs in higher education are presented in this article: (a) the concept of persistence is presented in two views (general and specific systematic); (b) meaning of concepts associated with non-persistence (non-persistence, dropout, attrition); (c) latest research related to persistence and non-persistence in doctoral studies according to “descriptive”, “theoretical” studies associated with the research and writing of the doctoral thesis (ABD all but dissertation); and (d) conclusions from two perspectives: the results of the document review and the justification and importance of doing research on this complex university phenomenon based on student’s personal views and opinions. We applied a methodological review of the papers, “literature review” for this study.