The theory of active systems - a section of the theory of management of socio-economic systems, studying the properties of the mechanisms of their functioning, due to the manifestations of the activity of the participants of the system During its development in the theory of active systems were developed,. Many effective management mechanisms have been researched and implemented, appropriate models and methods are used in solving a wide range of management problems in the economy and society - from the management of technological processes to decision-making at the level of regions and countries The present paper contains the classification of tasks of active systems management, an overview of the main theoretical results and a description of the experience of practical use of applied models, as well as a discussion of promising research areas. Extensive bibliography, including more than four hundred references, will allow the interested reader to more freely navigate the problems of the theory of active systems.