<p>The quantum cognition research program concerns the application of quantum probability theory (the rules for how to assign probabilities to events from quantum mechanics, without the physics) to cognitive modeling. We review quantum cognitive models in several areas of psychology, including conjunction/disjunction fallacies in probabilistic judgment, conceptual combinations, similarity, order effects on judgments, causal inference, the disjunction effect in decision making, measurement, and interference effects on judgments and decisions, memory, perception, and other judgment and decision-making applications. For each area, we first present the empirical findings that have motivated the application of quantum models, emphasizing any characteristics which are particularly puzzling or have resisted coherent theoretical explanations previously; we then discuss the quantum cognitive models, noting the key features of the models that help explain the empirical data; we finally cast a critical eye on the models and explore comparisons with non-quantum models.</p>