Cluster Analysis is aimed to detect groups in data. The presence of (even a small) number of outlying observations can be problematic when applying traditional Cluster Analysis methods. For instance, clearly differentiated clusters may be incorrectly joined and "spurious" clusters (composed of only few outlying observations) may be detected. Robust clustering techniques are designed to better resist these anomalous data values. This talk will focus on robust clustering procedures based on trimming. Trimming is a simple and easy to understand way to achieve robustness of statistical procedures. The proposed methodology attempts to discard (and thus detect) which are the most "anomalous" data entries by detecting an appropriate (not affected by outliers) clustering structure. It serves to clean data and also to detect interesting anomalies in our data that can then be investigated further. Methods for trimming entire observations (casewise) or just individual measurements (cellwise) are presented along with their adaptation to higher dimensional or functional data analysis problems.