How can people learn the meaning of a new word from just a few examples? What makes a set of examples more or less representative of a concept? What makes two examples of a category seem more or less similar? Why are some generalizations apparently based on all-or-none rules while others appear to be based on gradients of similarity? I will describe an approach to explaining these aspects of everyday induction in terms of rational statistical inference. In our Bayesian models, learning and reasoning are explained in terms of probability computations over a hypothesis space of possible concepts, word meanings, or generalizations. The structure of the learner's hypothesis spaces reflects their domain-specific prior knowledge, while the nature of the probability computations depends on domain-general statistical principles. The hypotheses can be thought of as either potential rules for abstraction or potential features for similarity, with the shape of the learner's posterior probability distribution determining whether generalization appears more rule-based or similarity-based. Bayesian models thus offer an alternative to classical accounts of learning and reasoning that rest on a single route to knowledge -- domain-general statistics or domain-specific constraints -- or a single representational paradigm -- abstract rules or exemplar similarity. This talk will illustrate the Bayesian approach to modeling learning and reasoning on a range of behavioral case studies, and contrast its explanations with those of more traditional process models.