An account is given of the current state of the problem of linear coupling between electromagnetic waves. Conversion effects are discussed for waves in the radio, optical, and x-ray frequency ranges in different inhomogeneous, weakly-anisotropic media, such as magnetoactive plasma (in the laboratory and in space), ``plasma + magnetized vacuum'' system, liquid crystals, ferroelectrics, lightguides, and so on. The linear coupling phenomenon arises when waves traverse an inhomogeneous portion of a medium in which dispersion curves converge and the wave polarization structure undergoes a change. A qualitative analysis is presented of linear wave conversion, which can be used as a basis for determining in a relatively simple manner the possibility and efficacy of wave coupling, and to exhibit the characteristic dependence of the conversion effect on the properties of the inhomogeneous medium. The qualitative analysis is accompanied by a discussion of the solution of a number of standard problems that are of interest in connection with specific applications of the linear wave-conversion effect.