We present a theory of electron, electromagnetic, and elastic wave propagation in systems consisting of non-overlapping scatterers in a host medium. The theory provides a framework for a unified description of wave propagation in three-dimensional periodic structures, finite slabs of layered structures, and systems with impurities: isolated impurities, impurity aggregates, or randomly distributed impurities. We point out the similarities and differences between the different cases considered, and discuss the numerical implementation of the formalism.