Psychological studies of categorization often assume that all concepts are of the same general kind, and are operated on by the same kind of categorization process. In this paper, we argue against this unitary view, and for the existence of qualitatively different categorization processes. In particular, we focus on the distinction between categorizing an item by: (a) applying a category-defining rule to the item vs. (b) determining the similarity of that item to remembered exemplars of a category. We begin by characterizing rule application and similarity computations as strategies of categorization. Next, we review experimental studies that have used artificial categories and shown that differences in instructions or time pressure can lead to either rule-based categorization or similarity-based categorization. Then we consider studies that have used natural concepts and again demonstrated that categorization can be done by either rule application or similarity calculations. Lastly, we take up evidence from cognitive neuroscience relevant to the rule vs. similarity issue. There is some indirect evidence from brain-damaged patients for neurological differences between categorization based on rules vs. that based on similarity (with the former involving frontal regions, and the latter relying more on posterior areas). For more direct evidence, we present the results of a recent neuroimaging experiment, which indicates that different neural circuits are involved when people categorize items on the basis of a rule as compared with when they categorize the same items on the basis of similarity.