This chapter surveys a variety of formal models of categorization, with emphasis on exemplar models. The chapter reviews exemplar models' similarity functions, learning algorithms, mechanisms for exemplar recruitment, formalizations of response probability, and response dynamics. A mutual goal of different formal models is to account for detailed quantitative data from laboratory experiments in categorization. Although a variety of representational formats have been formalized, exemplar models have been especially richly explored by researchers. The chapter discriminates numerous exemplar models to excise their functional components and to examine those components side by side. The main functional components include the computation of similarity, the learning of associations and attention, the recruitment of exemplars, the determination of response probability, and the generation of response times. This dissection revealed a variety of formalizations available for expressing any given psychological process.