Computational models will play an important role in our understanding of human higher-order cognition. How can a model's contribution to this goal be evaluated? This article argues that three important aspects of a model of higher-order cognition to evaluate are (a) its ability to reason, solve problems, converse, and learn as well as people do; (b) the breadth of situations in which it can do so; and (c) the parsimony of the mechanisms it posits. This article argues that fits of models to quantitative experimental data, although valuable for other reasons, do not address these criteria. Further, using analogies with other sciences, the history of cognitive science, and examples from modern-day research programs, this article identifies five activities that have been demonstrated to play an important role in our understanding of human higher-order cognition. These include modeling within a cognitive architecture, conducting artificial intelligence research, measuring and expanding a model's ability, finding mappings between the structure of different domains, and attempting to explain multiple phenomena within a single model. (Contains 1 figure and 1 note.)