This chapter addresses one important aspect of inductive reasoning, namely, psychological research on category-based induction, or how people use categories to make likely inferences. It describes similarity effects, typicality effects, diversity effects, and other phenomena, including background knowledge effects, setting the stage for the presentation of computational models of inductive reasoning. One consideration to keep in mind as computational models are presented is whether they have any facility for addressing not only similarity, typicality, and diversity effects, but also background knowledge effects and indeed whether they show any capacity for causal reasoning. The chapter discusses two general issues that arise in modeling inductive reasoning and also in computational modeling of other cognitive activities. The first issue is that cognitive activities do not fall neatly into pigeonholes. The second is that putting background knowledge into models is the necessary next step.