The present paper aims to familiarize with notions and concepts that belong to the phenomenon of giftedness. It deals with the complex phenomenon of giftedness, delimiting its content and scope, will be presented characteristics, theories, principles, models, forms of giftedness. A distinction must be made between genius, talent, creativity, giftedness and 'Olympians' Genius (a term little used nowadays), defined by creativity and exceptional ('epoch-making') performance in any field of scientific or artistic life. Talent is the expression of outstanding aptitudes, psycho-sensory and/or motor qualities and abilities, trained and manifested in various fields (scientific, artistic, social, sporting, etc.); Genius is "the highest stage of human spiritual endowment, characterised by a creative activity whose results are of great significance; the person who has such an endowment". However, as this explanation does not indicate the subversive implications of the idea of genius we turn our gaze, of course, to the great philosophers of the world who have theorized and explained the problem. Advanced learning for gifted children means acquiring information from different areas. They often follow their primary interest with a zeal not found in other children their age. The result is an outstanding academic achievement and a remarkable fund of information. The conclusion is also that such children need special learning conditions.