In this chapter, we consider the problem of scheduling time-constrained round-robin sports tournament problems, metaheuristics for its approximate solution, and their practical applications. This chapter uses graph theory as the fundamental tool. It presents a short introduction to its essential elements, definitions, and results relevant to the subject of this work. We also introduce the basic graph model used to represent single round-robin tournaments and the circle method for constructing timetables. We describe the different neighborhood structures that have been used in the literature of metaheuristics and local search procedures for scheduling time-constrained single round-robin sports tournaments: Home-Away Swap, Team Swap, Partial Team Swap, Round Swap, Partial Round Swap, and Generalized Partial Team Swap. They may be directly extended to double round-robin problems. We conclude by presenting a collection of applications of metaheuristics to sports scheduling problems.