Since the space, both virtual and real, available to drug discovery teams of potentially interesting compounds for synthesis is vast, clustering and diversity selection methods are essential in assisting the project teams to narrow down or broaden out the focus of the compounds to be purchased or synthesised. Many different algorithms exist to identify natural groupings of compounds or identify diverse compounds that cover a space of interest. Clustering algorithms are unsupervised statistical learning methods and can often be computationally intensive in their calculation and therefore a number of approaches have been proposed that can obviate the considerable computation, particularly to facilitate rapid analyses. A range of clustering and diversity selection algorithms will be presented in this chapter with consideration made to their appropriateness of application.