Abstract. This article discusses the theoretical, didactic, and methodological foundations for explaining the concept of function to students in mathematics education. The concept of function is one of the fundamental mathematical concepts directly related to algebra, geometry, mathematical analysis, physics, computer science, economics, and technical sciences. One of the important tasks of mathematics education is to ensure that students understand this concept not superficially, merely as a formula or a graph, but as a relationship between quantities, a correspondence, a process of change, and a means of modeling. The article analyzes the use of real-life situations in forming the concept of function, the establishment of connections among multiple representations such as tables, graphs, formulas, and verbal descriptions, the development of students’ conceptual understanding, the early identification and correction of errors, and the application of information and communication technologies as well as dynamic mathematical software. In addition, the importance of such principles as gradualness, visualization, problem-based learning, practical orientation, interdisciplinary integration, and a competency-based approach in teaching the concept of function is substantiated. The article also presents a methodological model for organizing a lesson, typical difficulties encountered by students, and ways to overcome them.