Competition and cooperation, which covered a variety of countries, there are not only in the sphere of economy, politics, but also in science. It is caused by the fact that the economic and political status of countries, the welfare of their populations are largely derived from the results of the scientific community in these countries. That is why one of the trends of development in several countries of the modern world, more recently, focused on maximum preservation tradition in economics, politics, social life, together with the adoption of a strategy to build and maintain in operational condition of the capitalist system of industrial relations has been the growing interest in innovation, to expand scientific activity. This study assesses the current trends in the development of science and innovation in Russia, identifies prospects optimize the functioning of the national innovation system. In the work are identified the main trends of development of science and innovation in the modern world, the attention paid to globalization and internationalization of research activities. Reveals the interdependence of content value imperatives of functioning using the capitalist mode of production, and the development of targets, which are put forward to science by society and the state in these countries. Comparative analysis of the historical experience of the research and innovation activities in Russia and developed countries shows the dominance of the role of the state and the militaristic nature of the national innovation system in Russia. Assessing the current state of the national innovation system shows a tendency of the Russian state to the preservation of the existing system and the direction of its functioning and in modern conditions. Analysis of the consequences of this policy allows us to assert that it could lead to further degradation of the national innovation system. The results show the need to choose a strategy of development of the national innovation system, in which the role of government should be to revitalize the other actors of the innovation system - private companies, entrepreneurs, universities and so on. It is necessary to create a competitive environment in the area of innovation, open access to resources for all subjects of the national innovation system.