Inductive reasoning entails using existing knowledge or observations to make predictions about novel cases. We review recent findings in research on category-based induction as well as theoretical models of these results, including similarity-based models, connectionist networks, an account based on relevance theory, Bayesian models, and other mathematical models. A number of touchstone empirical phenomena that involve taxonomic similarity are described. We also examine phenomena involving more complex background knowledge about premises and conclusions of inductive arguments and the properties referenced. Earlier models are shown to give a good account of similarity-based phenomena but not knowledge-based phenomena. Recent models that aim to account for both similarity-based and knowledge-based phenomena are reviewed and evaluated. Among the most important new directions in induction research are a focus on induction with uncertain premise categories, the modeling of the relationship between inductive and deductive reasoning, and examination of the neural substrates of induction. A common theme in both the well-established and emerging lines of induction research is the need to develop well-articulated and empirically testable formal models of induction. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website.