Recently, a lot of effort has been devoted to analyzing response dynamics in various games. Questions about the dynamics themselves and their convergence properties attracted a great deal of attention. This includes, for example, questions like “How long do uncoordinated agents need to reach an equilibrium?” and “Do uncoordinated agents quickly reach a state with low social cost?”. An important aspect in studying such dynamics is the learning model employed by self-interested agents in these models. Studying the effect of learning algorithms on the convergence rate of players is crucial for developing a solid understanding of the corresponding games. In this tutorial, we first describe an overview of the required terminology from game theory. Then, we survey results about the convergence of myopic and learning-based best responses of players to equilibria and approximately optimal solutions, and study the effect of various learning algorithms in convergence (rate). Throughout the tutorial, we describe fundamental connections between local search algorithms and learning algorithms with the convergence of best-response dynamics in multi-agent games.