Giftedness is defined as the innate tendency and ability of the child to achieve above average results in a scientific, practical-technical or artistic field. Defining giftedness is often changed by the concepts of talent, intelligence or creativity that can, but do not have to be, its definitions. There is an eternal question whether giftedness is innate or developed under the influence of the environment, so we must not neglect the quality of education of gifted students. Curriculum in a field of giftedness in the world and Croatia are based on accelerating, differentiating and enriching the curriculum with additional activities that would enable the full development of the potential of gifted students. The quality of teacher education is one of the main factors affecting the level of pupil's educational achievement. Therefore, education and professional development is a key issue in every country that seeks to improve the education system and make it more accessible and more flexible. Teachers’ personal characteristics and their access to learning and teaching contribute significantly to the learning outcomes as teachers are responsible for systematically encouraging motivation of their students, from pre-school to mature, to lifelong learning and mastering cognitive and social skills, thereby creating self-sufficient students with the necessity in investing in personal and professional growth and development.