This review contains a description of modelling studies relative to functionally graded materials (FGMs). Two principal topics are covered : models for microstructure-dependent thermophysical properties, and models for the design, processing, and performance of FGMs. The former is a particularly important input to FGM modelling because of the wide variety of microstructures that can exist across the graded direction of a single material. Based on the work described in this review, recommendations are made regarding areas in which additional modelling studies would be beneficial. Suggested approaches to the modelling include the application of a number of powerful techniques, such as percolation theory, fractal analysis, lattice-based microstructure models, the renormalization group, neural networks, and fuzzy logic.