Psychological and social sciences are currently intensely concerned with the study of personality and phenomena aimed at the problems of its development. The challenges of the ever-changing society require the formation of new personality skills, in order to cope with reality and new vital conditions. Responsibility today becomes a projective ability of the personality and a valuable personal resource in organizing one's own life and activities in accordance with personal goals and values. Responsibility is considered to be one of the fundamental principles of human existence and presents a higher formation – a complex phenomenon that characterizes personal and social maturity. In this article we mention the actuality and importance of studying the theme with reference to personality responsibility, we analyze the problem of personality responsibility in the context of multiple societal challenges; we highlight the psychological theories that explain the manifestation and development of personal responsibility. The multiple theoretical approaches, treat the problem of responsibility from various psychosocial perspectives and come to substantiate the formation of responsibility as a significant and complex dimension of personality. Also, in this context we describe, analyze and highlight the similarities and differences between the following theoretical approaches with reference to responsibility: theories of learning and social modeling; theory of psychosocial development of E. Eriksson, theory of J.B. Rotter about the locus of internal/external control, theory of self-actualization; resource theory, systemic approach to the study of personality Б.Г. Ананьев, Б.Ф. Ломов, approach to responsibility as a mechanism of semantic regulation, Д. Леонтьев, Е. Калитвиевская; approaches to personality resources as a factor regulating human activity and behavior, Л.Г. Дикая, Т.В. Корнилова, the theory of diffusion of personal responsibility within a group, substantiated by J. Darley and B. Latan, theories and concepts related to eclectic – integrative approaches. The psychosocial theories exposed will constitute a theoretical-scientific basis for the elaboration and promotion of an experimental research and a formative program for the development of personal responsibility, which we plan at the next stages of a complex research.