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Rational models of cognition aim to explain the structure of human thought and behavior as an optimal solution to the computational problems that are posed by our environment (Anderson, 1990; Chater & Oaksford, 1999; Marr, 1982; Oaksford & Chater, 1998). Rational models have been developed for several aspects of cognition, including memory (Anderson, 1990; Shiffrin & Steyvers, 1997), reasoning (Oaksford & Chater, 1994), generalization (Shepard, 1987; Tenenbaum & Griffiths, 2001), and causal induction (Anderson, 1990; Griffiths & Tenenbaum, 2005). By examining the computational problems that underlie our cognitive capacities, it is often possible to gain a deeper understanding of the assumptions behind successful models of human cognition, and to discover new classes of models that might otherwise have been overlooked. In this chapter, we pursue a rational analysis of category learning: inferring the structure of categories from a set of stimuli labeled as belonging to those categories. The knowledge acquired through this process can ultimately be used to make decisions about how to categorize new stimuli. Several rational analyses of category learning have been proposed (Anderson, 1990; Nosofsky, 1998; Ashby & Alfonso-Reese, 1995). These analyses essentially agree on the nature of the computational problem involved, casting category learning as a problem of density estimation: determining the probability distributions associated with different category labels. Viewing category