The dynamics of social, economic, and public life provide evidence of the increasing need to analyze current problems of children's education and giftedness. At present, work with gifted children in the municipal system of education is being conducted by many educational institutions--gymnasiums, lyceums, and institutions for supplementary education. Special-subject olympiads are being held on a regular basis, along with festivals and creative competitions, during which many talented and gifted children are found in various spheres of activity. There is a need to increase the intellectual potential of gifted children by creating favorable conditions in the municipal system of education. By enabling them to acquire a good education, it will be possible for them to achieve their potential and ensure their comprehensive development in various areas of intellectual and creative endeavor. The experience of the creation of a model gymnasium for working with gifted children in the Odintsovskii municipal raion of Moscow oblast shows how it may be possible to provide a more challenging education for these children. [This article was translated by Kim Braithwaite.]