Abstract: This article reviews the prerequisites for quantitative models of animal learning and cognition, describes the types of models, provides a rationale for the development of such quantitative models, describes criteria for their evaluation, and makes recommendations for the next generation of quantitative models. A modular approach to the development of models is described in which a procedure is considered as a generator of stimuli and a model is considered as a generator of responses. The goal is to develop models that, in combination with many different procedures, produce sequences of times of occurrence of events (stimuli and responses) that are indistinguishable from those produced by the animal under many experimental procedures and data analysis techniques.