This full day tutorial is an exposition of a rapidly growing new alternative approach to building computational models of cognition and decision based on quantum theory. 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; quantum probabilities do not obey the disjunctive axiom of Kolmogorov probability; quantum reasoning does not obey the principle of monotonic reasoning. It turns out that humans do not obey these restrictions either, which is why we consider a quantum approach. This tutorial will provide an exposition of the basic assumptions of classic versus quantum information processing theories. These basic assumptions will be examined, side by side, in a parallel and elementary manner.