After summarizing the basic theory derived in Atkin & Craine (1976α) we present constitutive theories for binary mixtures of fluids, a porous elastic solid and a binary mixture of elastic solids. Some applications of these theories are discussed, particular attention being focused on the viscometry of mixtures of viscous fluids and the propagation of small amplitude waves in the various classes of mixtures. Chemically reacting mixtures are also considered.