Increasing performance demand in a variety of applications of functionally graded materials makes the fracture behavior of such materials very important for assessing and enhancing the structural integrity. This paper briefly reviews previous works on FGMs and mainly focuses on mixed-mode crack growth in FGMs. In this paper, automatic simulation of crack propagation in functionally graded materials is performed by means of a remeshing algorithm in conjunction with the finite element method. The crack propagation is performed under mixed-mode loading. Each step of crack growth simulation consists of the calculation of the mixed-mode stress intensity factors by means of a novel formulation, so-called non-equilibrium formulation, of the interaction integral method, determination of the crack growth direction based on a specific fracture criterion, and local automatic remeshing along the crack path. A specific fracture criterion is tailored for FGMs based on the assumption of local homogenization of asymptotic crack-tip fields in FGMs. The present approach uses a user-defined crack increment at the beginning of the simulation. Crack trajectories obtained by the present numerical simulation are compared with available experimental results. The present work provides a basis for further investigation on cracked FGMs under thermo-mechanical loadings.