One of the key tasks of the authorities at all levels is to increase competitiveness and accelerate economic growth. In foreign literature, a lot of works are devoted to the study of innovations and their role in the development of states. A number of authors consider the problems related to the direct management of innovation systems, researching and analyzing from different points of view. The purpose of this article is to acquaint the interested circle of readers with the evolution of approaches to the management of innovative systems from the national level to the local one, with the current research results and their directions.