Quantum approaches to consciousness are sometimes said to be motivated simply by the idea that quantum theory is a mystery and consciousness is a mystery, so perhaps the two are related. The magnitude of the difference between the quantum and classical conceptions of the connection between mind and brain can scarcely be exaggerated. This chapter sketches out the transition from the classical physics conception of reality to von Neumann's application of the principles of quantum physics to our conscious brains. Classical physics arose from the theoretical effort of Isaac Newton to account for the findings of Johannes Kepler and Galileo Galilei. The core idea of the quantum approach is the seminal discovery by Werner Heisenberg that the classical model of a physical system can be considered to be an approximation to a quantum version of that model.