We present the results of a theoretical analysis of the psychological bases of success of athletes. We provide an overview of studies of the factors influencing the success of the activities in the sport. Sports activities are considered as a joint activity of athlete and coach, the success of which is affected by the personal qualities and characteristics of the relationship of its members. We summarize the main approaches to the study of personality and social psychological aspects of successful athletes and coaches. As the main factors in the success of sports activities, we considered individual psychological characteristics of athletes (motives, attitudes, modes of behavior and response), and socio-psychological characteristics of the interaction of coach and athlete (leadership style, the nature of interpersonal relationships and role expectations). We emphasize the importance of mutual role expectations of athlete and coach to achieve high results of sports activity.