The article substantiates the relevance of the problem of giftedness development for the 21st century education. The requirements put forward to a person in modern realities and the factors that define them are revealed. The problem relevanceis analysed on three levels: social-pedagogical, scientific-theoretical, practical-implementing. The tasks of giftedness development, which are outlined in the state educational policy, are presented. Modern approaches to the development of concepts and models of giftedness are studied: integrative, dynamic, humanistic. Examples of educational models that create conditions and opportunities for the development of students’ giftednessare considered. Problems related to the development of giftedness that require solutions in widespread practiceare identified.Possible directions for further research into giftedness as a pedagogical and social innovative task areclarified.

Keywords: giftedness development, common giftedness, integrative approach, dynamic approach, humanistic approach, humanistic educational model.