K-means is the most famous clustering algorithm. In this tutorial we review just what it is that clustering is trying to achieve, and we show the detailed reason that the k-means approach is cleverly optimizing something very meaningful. Oh yes, and we'll tell you (and show you) what the k-means algorithm actually does. You'll also learn about another famous class of clusterers: hierarchical methods (much beloved in the life sciences). Phrases like "Hierarchical Agglomerative Clustering" and "Single Linkage Clustering" will be bandied about.