The approaches to forming the national and regional innovation systems in Russia and other countries are analyzed. The necessity of applying the knowledge approach to the formation of innovative systems is justified. The factors that contribute to the successful development of the national innovation system are revealed: long-term innovative policy of the state; strengthening the cooperation between the private, educational and research sectors; targeted support of important directions for innovative and technological development; development of the innovative infrastructure to support innovative enterprises; improving the legislation in the field of intellectual property; accelerating the commercialization of innovation, providing tax incentives, cheap loans. The principles for the development of the national innovation system in Russia are proposed, including the decentralization of state support and the formation of a network of development institutions; using the mechanism of public-private partnership; building trust in new institutions through the personal reputation of managers; performing the support functions through business intermediaries; providing services instead of money. Instruments of coordination between the units of the national innovation system are designed. The mechanism of technological platforms for coordination between the units of the national innovation system is suggested. The necessity of coordination of federal and regional innovation policies is proved. The principles of forming regional innovation systems are proposed, including the development of innovative strategies and regional programs with the involvement of relevant scientific and educational organizations, companies, development institutions; formation and development of innovation infrastructure facilities; the introduction of public procurement to stimulate the production of innovative products; the development of innovative technologies and innovative management education programs. The necessity of forming regional innovation clusters is justified. Principles of forming the innovation system in resource-oriented regions are offered. A combined approach to the innovative development of the resource-oriented regions is designed. The institutions of the innovative infrastructure for resource-oriented regions are proposed.