The legal grounds for expertise in the scientific sphere are laid in the Federal Law “About Science and State Scientific and Technical Policy”, which states that public authorities of the Russian Federation and public authorities of the subjects of the Russian Federation organize the expertise of scientific and technical programs and projects financed by the corresponding budget. It is pointed out that there is a need for expert evaluation of the results of ongoing research and development in The Strategy for Scientific and Technological Development of the Russian Federation. The issues of organizing and conducting expert evaluations in certain areas of activity are sorted out on the basis of a number of “sectoral” federal laws, by-laws and methodological recommendations. Despitethe abundance of normative-legal documents, many fundamental issues related to scientific and scientific-technical expert activity remain unresolved yet. For example, the federal legislation does not define the procedure of organizing and conducting scientific and scientific-technical expertise, the relations between the participants, their rights and obligations. Meanwhile, much depends on quality and unbiased expertise in the scientific sphere, including the development of fair competition for resources. The authors seek to analyze from theoretical, legal and practical point of view the unresolved problems in the areas of scientific and scientific-technical expertise and its competitive component, and to make up appropriate recommendations, including those related to expert activity at the level of public authorities and in state funds supporting science. It is also proposed to come back to the issue of adopting a basic law on scientific and scientific-technical expertise, sipulating the leading role of the Russian Academy of Sciences in the independent expertise of scientific, scientific-technical and innovative projects.