A family of mixture models arises when various constraints are imposed upon component densities, and most often upon the covariance structure; the result is a flexible modelling paradigm that incorporates more and less parsimonious models. The “model-based clustering” is used to describe the process of clustering via a statistical model. However, it is often taken to mean the use of a mixture model for clustering or the use of a family of mixture models for clustering. Consider model-based discriminant analysis and suppose that each known class may correspond to multiple component densities in a mixture. Model-based clustering, classification, and discriminant analysis are best illustrated through their respective likelihoods. The Adjusted Rand index has become the most popular method for assessing class agreement in mixture model-based applications. However, the misclassification rate is sometimes used. The chapter also presents an overview of the key concepts discussed in this book.