The article is devoted to the history and current state of the school of Alexey Nikolaevich Leontiev (1903-1979), an outstanding Russian psychologist, the first Dean of the faculty of psychology of Moscow state University who have made the most significant contribution to the creation and development of the activity approach in psychology. Considered in detail the stages of scientific biography A.N. Leontiev, the author identifies and analyzes the main provisions developed his school of “non-classical psychology”, the origins of which date back to L.S. Vygotsky. Special attention is paid to the analysis offered in the school of A. N. Leontiev solve the problems of the subject of psychology, nature of psyche as a specific mental functions, the relationship between internal and external activities, units of psychological analysis and development of the psyche. Selected as promising lines of development of General psychological ideas of the school of A. N. Leontiev.