This chapter presents different formulations of the clustering problem using various optimization approaches. Namely, mixed integer programming, general nonsmooth optimization, and nonsmooth DC optimization-based formulations of the clustering problem are introduced together with models that improve the robustness, separability, and compactness of clusters. In addition, we formulate the auxiliary clustering problem and study optimality conditions for both the clustering and the auxiliary clustering problems. Finally, we discuss the smoothing of the clustering and the auxiliary clustering problems.