Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology. These processes are described by PDEs. The present monograph is a comprehensive study of homogenized problems, focusing on the construction of nonstandard models: non-local models, multicomponent models, and models with memory. Along with complete proofs of all main results, numerous examples are provided. Graduate students, applied mathematicians, physicists, and engineers will benefit from this monograph, which may be used in the classroom or as a comprehensive reference text.