The Frequency Assignment Problem (FAP) is a critical issue in telecommunications, involving the optimal allocation of frequencies to transmitters under various constraints. This chapter provides a comprehensive overview of the FAP, starting with a formal definition and highlighting its complexity, including its classification as an NP-hard problem. The relationship between FAP and graph coloring is explored, showcasing how graph theoretical approaches can be applied to model and solve the problem. Various optimization objectives, such as minimizing interference and spectrum usage, are discussed. The chapter also reviews related work, emphasizing the evolution of algorithms and methods, particularly in the context of cellular networks, where minimizing interference is paramount. Finally, alternative formulations and advanced heuristics for solving the FAP are examined, offering insights into both theoretical and practical aspects of this complex problem.