The transformation of international relations, economics, scientific views, and technologies of production and communication implies the processes of involvement and social and academic integration. Introduction of new international standards for Russian higher education and establishment of the federal project 5/100/2020 to boost the global competitiveness of Russian universities in order to break into the top 100 in the World University Rankings (THE, QS and ARWU) affect the reputation of universities. The paper reports on the place of Russia in the global market for education services, primarily of tertiary level, and on changes in the training of foreigners over the last twenty years. The key indicators of training of foreign students in Russia affecting the position of Russian universities in global rankings have been considered. The paper presents statistical data on the number of quotas for admission of foreigners to study in Russian universities at the expense of the Russian budget and satisfaction of foreign students with living conditions.