The paper discusses the difficulties that arise in identifying gifted students at the elementary school level. It is emphasized how important it is to recognize and support gifted individuals within the educational system. Theoretical part discusses various meanings and frameworks of giftedness such as Renzulli's three-ring theory, Sternberg's triarchic theory of intelligence and Tannenbaum's Sea Star Model. The giftedness of primary school children is shown by myths about the gifted, their characteristics, but also by how important early identification is. Learning difficulties such as ADHD, Asperger’s syndrome and dyslexia can also hide giftedness. Paying attention to the emotional characteristics of gifted students is crucial, with a focus on managing and understanding intense emotions. Pedagogues play a key role in the identification of gifted students and providing support. Professional competences of pedagogues are as important as cooperation with teachers in identifying gifted students. Different approaches are suggested for working with the gifted, such as grouping based on abilities, enriching the curriculum, accelerating the pace of learning and applying the differentiation technique. The paper emphasizes the support gifted students need, both academically and emotionally. The goal is better understanding of recognition of giftedness despite the difficulties that can hide it and how pedagogues and teachers, through their teamwork, can largely contribute to the development of gifted students to their full potential.