In a wide range of fields of natural science and technology, problems arise related to the study of the properties of heterogeneous media and the processes occurring in them. Especially great interest in their research has recently appeared in connection with the design of composite materials and the optimization of their characteristics. The book deals with mathematical models of problems of the theory of elasticity, heat transfer, energy transfer by radiation and wave propagation in microhomogeneous materials, diffusion and filtration in a porous medium; continuum models of lattice structures are obtained. The result of the ongoing constructions, in particular, are mathematically sound algorithms for determining the average and local characteristics of environments based on information about their microstructure.