Introduction. This article discusses the most relevant issues of gifted children education in basic and additional general educational programs. It focuses on constitutional and legal regulation of gifted children education in the Russian Federation. Discussion. The article explores the category of gifted children, reveals its essential characteristics and specifics of consolidation in national legislation. The authors analyze norms of political and legal documents and legislation in the field of education of the Russian Federation. The norms regulate the organization of gifted children education, children’s participation in olympiads, creative contests and other events. The experience of a number of foreign countries is studied in terms of obtaining education for gifted children including peculiarities of identifying and supporting talented children. Conclusion. The authors determine the necessity of creating a special system for identifying and supporting gifted children in mathematics, physics, history, drawing, music, etc. Furthermore, a comfortable environment for the manifestation, development, stimulation of children’s abilities, and training (retraining, advanced training) of teachers are also in need.