This research deals with the theoretical prediction of the overall or effective behavior of nonlinear composite materials undergoing large deformations. In particular, applications are envisaged to the high-temperature creeping behavior of metal/metal, metal/ceramic composites, and to porous materials. Both isotropic and anisotropic configurations are considered including the technologically important case of fiber-reinforced composites. The approach is based on new variational principles developed recently by the author (under AFOSR sponsorship), which allow the estimation of the overall behavior of a given nonlinear composite in terms of the effective properties of a suitably optimized linear comparison composite (with the same microstructure). The key advantage of the method is that it allows direct application of the extensive literature on linear composite materials, in the form of estimates of various types and rigorous bounds, to obtain corresponding results for nonlinear composites. Additionally, the procedure is remarkably simple to implement, and the final results are usually expressed in terms of finite-optimization problems, which can be readily solved with little computational effort. Recent progress includes the application of the method to the computation of the effective behavior of anisotropic systems, including laminated and fiber-reinforced nonlinear composites, and to the determination of extremal yield surfaces for rigid/plastic systems.