We consider the origins and development of the concept of higher education internationalization in the context of globalization processes; the main stages in the concept formation are identified. A substantial increase in the significance of comprehensive internationalization processes for developing and maintaining the international competitiveness of universities in the global knowledge society is demonstrated. Key motives and functions of internationalization are examined. Principal mechanisms for effective internationalization of higher education institutions in modern conditions are described. There is presented a case study of internationalization of National Research Lobachevsky State University of Nizhni Novgorod, a participant of the «5-100 Program». We characterize the main technologies applied for UNN internationalization in the course of the last twenty-five years, including the role of internationalization in the strategy of university development and management, as well as the mechanisms involved in the internationalization of education, and organization of work with international students. The key results and the prospects for further development of university internationalization processes in the context of enhancing its competitiveness among the world's leading science and education centers are discussed.