Coupled atmosphere-ocean models are at the core of numerical climate models. There is an extraordinarily broad class of coupled atmosphere-ocean models ranging from sets of equations that can be solved analytically to highly detailed representations of Nature requiring the most advanced computers for execution. The models are applied to subjects including the conceptual understanding of Earth's climate, predictions that support human activities in a variable climate, and projections aimed to prepare society for climate change. The present book fills a void in the current literature by presenting a basic and yet rigorous treatment of how the models of the atmosphere and the ocean are put together into a coupled system. The text of the book is divided into chapters organized according to complexity of the components that are coupled. Two full chapters are dedicated to current efforts on the development of generalist couplers and coupling methodologies all over the world.