The article considers the issue of the personality identity crisis in the situation of social instability and discusses the topicality of the phenomenon. It is shown that crises constantly occur at certain stages of development of a person, group, society as a whole or in different spheres of a social life, but at the same time they have their own uniqueness and significance. The crisis is considered as a problem that cannot be avoided, but also cannot be resolved with the available means. Personal identity is understood as an internal, self-created, dynamic organization of needs, abilities, beliefs and individual history. In modern conditions of uncertainty and instability, contradictions that exist in the image of the world by the people are intensified to the maximum and have a destabilizing effect on their emotional state and physical well-being. The uniqueness of the situation is that the scale of the threat is equal to the total population of the globe, the threat is inevitable and extraordinary in its consequences. Humanity has never faced such a situation in its history. The author notes that for all scientific approaches in the frame of which the problem is studied, the common thing is that in the process of identity formation, a person discovers himself / herself and his /her place in the world, its main function is to maintain stability, certainty, continuity, and the integrity of the personality. The article identifies and examines the causes of the modern identity crisis that accompanies globalization processes in the world, describes the types, stages, features of a person's situational reactions to the crisis, psychological features of the manifestations of identity in crisis situations at the emotional, cognitive, and behavioral levels. It is concluded that, to a significant extent, the identity crisis, its dynamics, the scale in which it is presented in the modern world is a consequence of globalization processes leading to the disintegration of traditional social ties, which were the basis of stability in previous conditions. Today the task of choosing a “life project” for oneself, constructing and adapting an identity is becoming urgent.