The Maunder Minimum was a period of very low solar magnetic activity and a near absence of sunspots, that occurred between 1645-1715 AD. The solar luminosity decreased by an estimated 1%, and pronounced cooling of the Earth’s climate during that time is evident in both historical and geological proxy records. Current global climate model(GCM) simulations do an excellent job of reproducing the Northern Hemisphere climate during the Maunder Minimum, and can also be used to predict what might happen to the climate system if another Maunder Minimum were to occur later this century. A future Maunder Minimum in solar activity would cool the climate system somewhat on the global average, but would not offset the overall climate warming we are seeing from greenhouse gas increases. Analysis of magnetic activity in solar type stars suggests that these periods of very low magnetic activity are rare, with the Sun spending perhaps 5% of its main sequence lifetime in a Maunder Minimum state.