The question of how one should decide among competing explanations of data is at the heart of the scientific enterprise. Computational models of cognition are increasingly being advanced as descriptions and explanations of behavior in the cognitive sciences. The success of this line of inquiry depends on the availability of robust quantitative methods to guide the evaluation and selection of these models. The purpose of this tutorial is to introduce methods of evaluating and selecting among mathematical models of cognition. Our goal in the tutorial is to provide a good conceptual overview of methods of model comparison with illustrative examples using selected models in cognitive science.