The article studies the phenomenon of internationalization of higher education. It turns out that globalization is the background for the development of the internationalization of education. Problems of internationalization of education are analyzed, including the problem of multicultural education, strategies of internationalization of higher education, the problem of intercultural communication. It is emphasized that the phenomena of "encapsulation" and "dissolution" are risks in the way of internationalization of education. It is noted that the student environment is turning into a wide, global space for direct interaction of large masses of representatives of various cultural forms and traditions. The experience of Borys Grinchenko Kyiv University in this direction of scientific and pedagogical activity is studied. The article is based on the program documents of the educational space of the European Union. It is substantiated that the internationalization of higher education contributes to the formation of the "knowledge society". The problems and challenges of the process of internationalization of higher education in Ukrainian society are determined.