Mathematics, in addition to be a scientific discipline, is also known as one of the main and compulsory subjects in primary and secondary school. Mathematics is often known as one of the most difficult subjects for many students, and the acquisition of knowledge in mathematics will be demanding and often troublesome. However, some students show a special affection and motivation for learning mathematics. These can be above – average students who show interest in mathematics but also mathematically gifted students. This paper aims to raise awareness of the importance of mathematically gifted students in the education, starting from early detection and support to longitudinal monitoring through lifelong learning. The first part of the paper starts with definitions of giftedness. Based on various theoretical models and brief overview of the characteristics of gifted children, the goal is to describe their specifics and needs as clearly as possible. It further clarifies how mathematical giftedness is perceived in the professional and scientific community. The way of working with gifted students and characteristics of mathematically gifted students is preceded by a description of mathematics as a discipline, which makes it easier to understand the specifics and needs of gifted students in mathematics. A very important part of this paper is the chapter dedicated to the identification of gifted students. Certain stages that need to be passed are listed, as well as the instruments that are used in the detection of gifted students. The most comprehensive part of the work is the one dedicated to working with gifted students. There are emphasized goals that should be a priority in education of gifted students and the importance of educational system in that. Special attention is dedicated to the methodology of working with mathematically gifted students and didactic system aimed at developing their abilities, the way of learning and problem solving. Accordingly, there are presented important key competencies for teachers, so that they can successfully teach and collaborate with mathematically gifted students.