This monograph presents both continuum and mathematical treatments of nonlinear electromechanical couplings in dielectric media with applications to piezoelectric and ferroelectric crystals, piezoelectric powders and solutions of electrodeformable macromolecules. The authors treat a variety of static and dynamic nonlinear effects which currently have engineering applications. They also provide an insight into the nonlinear behaviour of new materials such as ferroelectrics, powders and ceramics. The mathematical treatment includes asymptotic expansions, singular perturbations, hyperbolic systems, convexity and soliton theory.