Functionally graded materials feature gradual transitions in microstructure and composition which are engineered so as to meet functional performance requirements that vary with location within a single component and to optimise the overall performance of the component. This monograph constitutes a revised, expanded, updated and integrated collection of two review articles by the authors which appeared in International Materials Reviews. An emphasis is placed on the fundamentals of processing and thermomechanical response of graded metals and metal/ceramic composites, in an attempt to maintain an adequate depth of coverage of a reasonably broad range of topics including process metallurgy, composite synthesis, the mechanics and micromechanics of composites, and fracture mechanics. The applications of fundamental principles to practical situations are also pointed out wherever appropriate.