The research interest to such phenomenon as giftedness has already been taken place in the discussions in some areas: anthropological about human nature, pedagogical about the interaction between bringing up, education and training of a gifted child, social about the circumstances of revealing of special abilities of children, psycological about nature, classification and sources of giftedness. On the base of theoretical-empirical methods of scientific research (theoretical analysis of philosophical, pedagogical, psychological, methodical, historical literature; content-analysis of normative-methodical documents, methods of comparison and classification) the following results of retrospective analysis of theories of giftedness. The stages in the development of the idea of giftedness and its fundamental distinctive definitions are highlighted, the methodical principles of theories of giftedness are defined, the necessity of working out the methodological basis of the process of continuous development of gifted children. The retrospective analysis of evolutional development of the theories of giftedness points out that their conceptual differences are based on different scientific theoretical and methodological researches, are determined by the dynamics of socio-political, economical and socio-cultural processes. On the other hand, the diversity of concepts is the consequence of versatility and difficulty of giftedness nature, impossibility to work out the general references and strategies of development for all its demonstrations. The giftedness is defined as gradually developing competence, performing as the basis of effective activity of the talented personality. The study, analysis and generalization of the main elements of the giftedness theories given in the works of Russian and foreign scientists, form the scientific platform for search and working out the scientific and practical methods of giftedness development aimed to find out and develop of potential and hidden opportunities of schoolchildren, aimed to individual accompaniment of their educational paths, aimed to formation of social motivation.

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