In this chapter, we describe two clustering algorithms for robust clustering. These algorithms are based on a (soft) trimming approach, utilizing only the most significant points to identify the cluster structure. The first algorithm, the trimmed k-means, can be seen as a modification of k-means toward robustness, while the second algorithm, the robust clustering algorithm RClus, uses soft trimming and is based on nonsmooth optimization approaches. In addition, it applies incremental approaches to find good-quality starting points. Detailed descriptions and step-by-step formulation of these algorithms are given.