Understanding and predicting the Earth's climate system, particularly climate variability and possible human-induced climate change, presents one of the most difficult and urgent challenges in science. Climate scientists worldwide have responded to that challenge over the past decade by creating a wide variety of ever more sophisticated climate models that are beginning to show considerable ability to replicate many aspects of the climate system. At the same time, to fully understand climate change, one also has to look to past climates. For this purpose, five eminent scholars who span the disciplines of modeling and observation, including elements of past, present and future climate studies came together at this Les Houches school. They presented a systematic development of each of their respective subjects which provided a comprehensive overview of this vast and complex subject. These core lectures were supplemented by a set of shorter lectures and of seminars.