The modern trend of education development is digitalization, transition from conventional classroom offline model to distance online education. Formation of global digital society was accelerated due to the COVID–19 pandemic, when significant portion of Earth population, including students, was forced to work, to study distantly. In this regard, this article discusses the responses of Russian system of higher education to current challenges of digitalization. This article analyzes interactive educational technologies of online, digital, e-learning, visualization and gamification of education, implementation of network structures. On the basis of analysis of the modern state of Russian higher education, the unsolved key issues are demonstrated as well as the main trends of the required changes. This work describes the urgent issues of development of regulatory framework of digital education, intensification of development of digital infrastructure of universities, digital training and further training of teachers and students, analysis and actualization of existing specialties and fields. Solution of the mentioned issues requires for legislative, organizational, administrative, technological, teaching and learning efforts of the country, universities, and society. A response of the Russian system of higher education to the challenges of digitalization can be comprised of formation of unified information and education portal of national universities, designing a model of digital university.