The article investigates the problems of formation and development of the world-class universities in Russia in the context of the strategic goals of modernization of Russian higher education, that were stated in the Russian President's Decree No. 599 of May 7, 2012 On the measures of the state policy implementation in the field of education and science. The paper examines key factors and conditions for formation and development of the world-class universities in Russia as well as the strategies how to improve global competitiveness of the national universities in Russia. The article also reviews the projects targeting the achievement of Russian government’s goal of having at least five Russian universities ranked within the global top 100 by 2020.