Twelfth Arnold Sommerfeld Lecture Series, The last three decades have witnessed the discovery of many new superconductors, with properties dramatically different from the conventional low temperature superconductors described by the Bardeen-Cooper- Schrieffer theory. These new superconductors can have much higher critical temperature, and all display antiferromagnetism in their phase diagrams. I will introduce the theory of quantum phase transitions, and use it to interpret recent experiments on these materials.