Previous chapters have set up various tools for understanding and analysing the ingredients of optimization problems. In particular, we have discussed the existence of solutions and characterizations thereof. This chapter discusses the powerful notion of associating a problem in the dual space with a given optimization problem (in the primal space). As it turns out, this notion proves valuable in practice. We will also discuss general and frequently encountered special classes of optimization problems, such as linear and quadratic programs, as well as non-linear optimization and difference-of-convex programs.