The authors make an attempt of solving the task of providing the students with a possibility to assess the quality of the organization and content of the higher education. The authors consider the Russian and Western practices of engaging students in such assessing activities as one of their main actors. The article identifies the most common forms of student participation in ensuring the quality of education, some of its problem areas and unused resources. Thus, the basic form of student participation in evaluation and control activities in the university is to fill out various questionnaires in order to express their assessments and opinions about the courses taken during the training period. The authors considered some relevant practices of foreign and Russian universities, in particular, the experience of the RUDN University, North-Eastern Federal University, Institute of Quality Student Commissioners of the Kemerovo branch of the RSTEU, and the Center for Applied Sociological Research of the MPEI. The article presents the results of the sociological study of opinions and assessments of the MPEI graduates in technical and social-humanitarian areas, which was conducted in 2017-2019 on the issues of basic and professional training. The monitoring study revealed a number of factors that affect the quality of practical training at the university, which allowed the authors to identify the key problems of marketing educational services by the contemporary university and to show the need to study the issues of self-realization of graduates, their demand in the labor market, and to search for new criteria for assessing the quality of higher education. The authors believe that we need a new ideology of quality management in the higher education, and propose some conditions and measures that would ensure the high quality of the higher education in Russia.