The article analyzes modern research on the effectiveness of the application of different teaching practices for gifted and talented students based on acceleration and enrichment strategies. The data of foreign studies on the size of the educational effect on academic success, social and personal development of gifted and talented students, depending on the applied strategies and training programs, as well as educational levels, are discussed. The positive influence of most forms of acceleration and enrichment on the academic success of gifted students can be considered proven, although the size of the effect is different for different forms and different levels of education. With regard to the socio-emotional and personal development of gifted students, the data on the positive impact is not so clear, while enrichment programs have an advantage, and the maximum effect size is shown for high school students. The problem of the lack of empirical data on the effectiveness of enriched programs for gifted students and most of all for gifted elementary school students has been identified. An example of the implementation of the enrichment strategy for gifted children of this educational level in domestic practice is presented — the program of creative interdisciplinary training “The gifted child”, which has a sufficient, although not complete, evidence base. Its wider implementation and distribution is associated with the problem of psychological and pedagogical training of teachers. The article presents.