Abstract：Functionally Graded Materials (FGMs) are new composites which are able to satisfy the harsh requirements for the materials used in the high-technology fields, such as astronautics, aeronautics, national defense, etc. Since FGMs are multiple phase materials with the properties of spatial and continuous variance, they could maintain the structural rigidity, reduce the thermal stress, and resist the severe thermal loading from the high temperature environment. The extensive usage of the FGM promotes the development of fracture mechanics. A description of studies related to fracture mechanics problems of FGMs is presented, and in where four principal topics are covered, that is, static and dynamic fracture mechanics problems, thermal elastic fracture mechanics problems, and the experimental works for investigating the fracture of FGMs. Finally, recommendations are made with regard to the areas in which additional work should be done. The research on the FGMs is of great significance for optimizing the design of FGMs.