In this article we propose and test a rule-plus-exception model of classification learning called RULEX. According to the RULEX model, which is formalized in a computer simulation, people learn to classify objects by forming simple logical rules and remembering occasional exceptions to those rules. In contrast to numerous extant models, complete exemplars are rarely stored as part of the category representation. Because the learning process in RULEX iS inherently stochastic, the model predicts that individual subjects will vary greatly in the particular rules that are formed and the particular exceptions that are stored. Averaged classification data are presumed to represent mixtures of these highly idiosyncratic rules and exceptions. We demonstrate that the RULEX model is able to account for numerous important phenomena in the classification literature, including prototype effects and specific-exemplar effects, sensitivity to correlational information, the difficulty of learning linearly separable versus nonlinearly separable categories, selective attention effects, and the difficulty of learning concepts with rules of differing complexity. In addition, we introduce the idea of testing models on their ability to predict distributions of classification responses at the individual subject level. Beyond accounting for these phenomena at a qualitative level, we demonstrate that RULEX is able to achieve reasonable quantitative fits to the data.