Abstract: The principle of optical cloaking, first published in Science in 2006, has been quickly extended from light waves to acoustic, seismic, and water waves, as they all obey the wave equations. Because thermal conduction satisfies diffusion equations as well as wave equations, and the former have different physical mechanisms, the extension from optical cloaking to thermal cloaking is a greater challenge. Thus, research on thermal metamaterials has been very slow. As early as in 2008, various counter-intuitive functions and properties like thermal cloaks and thermal inverters were proposed on the basis of finite element simulations, and the concept of thermal metamaterials was introduced. However, this concept was only demonstrated experimentally in 2012. On account of their potential applications, thermal metameterials soon received much attention from the international community. The main aim of this review is to describe this new type of functional material——thermal metamaterials. We shall present an overview of their physical principles, history, and progress in both theoreical and experimental research.