The coexistence of the phenomena of digitalization and law determines their mutual influence and actualizes the scientific task of studying the impact that manifests itself in relation to each other and the changes that it causes. The technicalization of society contributed to its further development, its goals and directions were largely determined by public and other social institutions, including law. In the modern period, digitalization is in the same vein of combining social and technical mechanisms for managing processes in society, moreover, in a wide socio-economic context and in connection with the implementation of the state's strategic national goals. A noticeable influence of similar phenomena and processes is observed in foreign countries. These circumstances predetermine the challenges for the law. The article presents an attempt to consider the legal problems of digitalization from the point of view of a comprehensive, cross-sectoral and systems analysis, which made it possible to overcome the excessive specialization of legal sciences' branches, keep in mind the dynamics of the relationship between national and international law and also take into account the context of the achievements of other social sciences. New digital technologies fill the functional impact of law with new content, which, firstly, is reflected in the dynamically developing sectoral legislation, and secondly, in a concentrated form it is manifested in the formation of general regulatory legal acts that create the basis for digitalization. Digitalization transforms the nature of the activities of legal entities and the volume of their legal relations, generates new forms of making managerial decisions and responsibility for their failure, problematizes the legal nature of a technical (electronic) legal act and its place in the system of normative legal regulation, raises the question of the possibilities and limits of automation of law. As a result of the study, the authors come to the conclusion that in the context of the digital transformation of the economy, social sphere and governance law retains its stable role as a regulator of socio-economic and other processes in society, ensuring both sustainable stability and the necessary transformative activities of people and public institutions.