We assessed the level of internationalization of Russian universities by different criteria, determined the influence of the indicators of internationalization on the attractiveness of universities and their competitiveness, identified the problem aspects of the considered process, and substantiated recommendations for their resolution. The study is based on the institutional approach, which includes the aspects of education, international cooperation, and dissemination of knowledge and ideas. The proposed methodological basis is supplemented with the theories and practices of the sphere of organizational change, state regulation, pedagogical sciences, etc. The main methods used in this study represent the general scientific domain, as well as the special methods of statistical research, such as the index method, average values method, method of determination of deviations, etc. This study considered the essence and components of the internationalization of universities, the state of the internationalization of Russian universities according to absolute and relative indicators, and compared with ranking indicators. According to this, we determined the problem aspects of their internationalization and outlined the prospects for their resolution and further development of Russian universities in the conditions of an increase in the globalization of education and science. We identified the problem of imbalance of the indicators of the internationalization в universities with the highest rankings, which involves the use of complex actions for improving the most problematic spheres of the activities. This concerns the development of faculties with international specialization and the improvement of the level of Internet presence of Russian universities in the global educational space.