The aim of this paper is to analyse, provide information on and an overview of research on giftedness and gifted children and on potentials in terms of the development of the approach and method of working with them. In addition to defining the basic concept of giftedness, the paper also specifies the importance of identification of gifted children for the purpose of applying the necessary approach and appropriate method of working with them for further development in accordance with their needs. Koren (1988) defines giftedness as a set of qualities that enable individuals to consistently achieve distinctly above-average results in one or more activities they are involved in. It is important to familiarise educators and parents with this concept and inform them about the importance of recognising giftedness and of working with gifted children, as well as of applying the appropriate method of working with them in educational institutions. The paper presents information on basic characteristics of giftedness, early signs and identification of giftedness and methods and approaches of working with gifted children. Based on review of existing surveys, solutions are presented which could help educators and parents in working with gifted children. Knowledge about and familiarisation with the concept of giftedness would mean great progress in the work of educational institutions, but also in the development of gifted children. The development of children’s giftedness can only occur in an organised and stimulating environment, part of which are both educators and parents, which is why their education is important.