In this chapter we introduce the clustering problem and use it to motivate mixture models. We start by describing clustering in a frequentist paradigm and introduce the relevant likelihoods and latent variables. We then discuss properties of the likelihoods including invariance with respect to label swapping. Finally, we expand this discussion to describe clustering and mixture models more generally within a Bayesian paradigm. This allows us to introduce Dirichlet priors used in inferring the weight we ascribe to each cluster component from which the data are drawn. Finally, we describe the infinite mixture model and Dirichlet process priors within the Bayesian nonparametric paradigm, appropriate for the analysis of uncharacterized data that may contain an unspecified number of clusters.