This article presents intellectual context for computational modeling, namely the manner in which it fits into the collective enterprise of advancing modern social science theory, and also assesses the claims made by critics and proponents of computational modeling in the social sciences, with a special focus on complexity models. Prediction takes a back seat for the most influential mathematical models from the social sciences. Computational models can be tools for explanation. Inductive-statistical (IS), deductive-nomological (DN), causal-mechanical (CM), and causally relevant (CR) explanations have both insight and prediction as elements of scientific explanation, though they vary in their emphases. The article then turns to computational models, and specifically models in the complexity tradition. There is little doubt that computational models permit the analysis of the aggregation of behaviors of diverse, adaptive agents which might alter their decision rules in response to aggregate patterns better than other modeling methods, especially game theoretic models.