No two health care systems are alike yet there are many questions common to all. What is a market and how do markets work? Why do markets for health care fail so badly when left free of government intervention? If (or rather, when) governments do intervene in health care, what should be their objectives and what form should intervention take? What is the balance between efficiency and equity? Several types of systems exist along with different mechanisms within systems. These are comprehensively reviewed with an eye to their success as well as challenges for the future to both health care systems and health economics research.