The review is devoted to effects that occur when waves propagate in inhomogeneous media. The types of linear transformation of waves by the inhomogeneities of the medium are classified, and the conditions under which they are realized are indicated. Linear transformation of oscillations in a non-equilibrium medium, leading to wave amplification, is investigated. The linear transformation is consistently analyzed on the basis of a fourth-order differential equation. Attention is called to the singularities of linear wave transformation in a plasma-beam system, particularly the anisotropy of the radiation of transverse waves following passage of a modulated beam through an inhomogeneous plasma. The generation of the second harmonic of an electromagnetic wave in an inhomogeneous plasma and decay processes in inhomogeneous media are considered. Kinetic nonlocal effects (of the echo type) in an inhomogeneous plasma, wherein the focusing action of the inhomogeneity makes possible linear nonlocal effects as well as echo at the summary frequency are described. The indicated nonlinear and kinetic nonlocal effects lead to ``transparentization'' of the inhomogeneous media. Certain experimental studies dealing with the problems touched upon in the review are discussed.