This chapter is devoted to the description of some general methods of nonsmooth optimization. The first two—the standard subgradient and the proximal bundle methods—form the basis for numerical nonsmooth optimization. In addition, we will focus on methods that are used in clustering algorithms given in Part II of this book. They are the limited memory bundle method, DC diagonal bundle method, nonsmooth DC method, DC algorithm, discrete gradient method, and the method based on smoothing techniques. For each of these methods, we present a flowchart, give some clarifying explanations, and study convergence properties.