At the beginning, this paper explains the notion of giftedness and various aspects in which giftedness can be observed. It also introduces usual views of people about the notion of giftedness, but also some frequent and, unfortunately, deeply rooted myths about the gifted children in which some people believe. In order to better understand the development of educational approaches to gifted children, this paper describes the notions of giftedness and gifted children through history and consequently introduces a proper approach to gifted children. It also describes the art giftedness in general as well as the phases of artistic expression of children from early childhood. Also, it describes signs and characteristics of artfully gifted children and gives their specific behaviours and difficulties in integration in society. Furthermore, it describes desirable procedures of educators, in the approach and manner of their work with such children in the educational groups. Most gifted children have a high IQ and their visual-spatial intelligence is particularly developed. Therefore, when we have reasons to believe a child is gifted, it is best to test the child in an area where they have shown remarkable abilities, in this case in art, in order to continue to work in the best possible way and provide them with regular observation and encourage their further creation and development to meet their specific educational needs. The importance of bringing works of art to children who are artgifted, as well as to children in general, is emphasized because it helps them understand what man can create with his imagination and ideas. It can also act as an incentive for their artistic expression and creation. In the further development of a child's artistic ability, the role of educators who have to develop the child's ability using various appropriate principles in their work is crucial. The most important are individual approach and differentiated approach, as well as humour and encouraging their divergent thinking.