This tutorial covers the rapidly growing new approach to building computational models of cognition based on quantum theory. The cognitive revolution that occurred in the 1960’s was based on classical computational logic, and the connectionist movements of the 1970’s were based on classical dynamical systems. These classical assumptions remain at the heart of both cognitive architecture and neural network theories, and they are so commonly applied that we take them for granted and presume them to be true. What are these critical but hidden assumptions upon which traditional theories rely? Quantum theory provides a fundamentally different approach to logic, reasoning, probabilistic inference, and dynamical systems. For example, quantum logic does not follow the distributive axiom of Boolean logic, and quantum probabilities do not obey the disjunctive axiom of Kolmogorov probability. It turns out that humans do not obey these restrictions either, which is why we consider a quantum approach.