This paper reviews the main psychological phenomena of inductive reasoning, covering 25 years of experimental and model-based research, in particular addressing four questions. First, what makes a case or event generalizable to other cases? Second, what makes a set of cases generalizable? Third, what makes a property or predicate projectable? Fourth, how do psychological models of induction address these results? The key results in inductive reasoning are outlined, and several recent models, including a new Bayesian account, are evaluated with respect to these results. In addition, future directions for experimental and model-based work are proposed.