The neurophysiological mechanisms underlying social behavior are still poorly understood. An increasing number of international studies uses hyperscanning for simultaneous recording of brain activation from several individuals during social interaction. Despite the outstanding school of Russian social psychology, the number of studies investigating the neurophysiological basis of social behavior in humans is still limited in the Russian literature. The goal of the present work was to review the hyperscanning methods, i.e., methods for simultaneous recording of physiological indices used to investigate inter-brain synchronization during social interactions. The paper discusses methods for recording and analysis of multi-subject data representing the changes in brain activity, existing experimental and naturalistic models, key results, as well as applied and fundamental aspects of the implementation of this technique in social psychology and neuroscience. Introduction of the methods which allow for a better understanding of physiological mechanisms of social interactions may significantly contribute to the development of innovative approaches to improving educational process, teamwork in various professional areas, social welfare, and psychosomatic health of people.