The interaction of electromagnetic waves with free-carrier plasmas in semiconductors and semimetals is analysed, with particular emphasis on microwave and infrared effects arising in the presence of external magnetic fields. The general frequency- and field-dependent dielectric tensor is initially developed for a single isotropic band via the Boltzmann equation in the local approximation. Solution of the electromagnetic wave equation in the tensor medium yields two normal modes, whose complex propagation constants and polarizations are determined by the microscopic medium parameters as well as the angle θ between wave vector q and applied magnetic field B₀. We first consider wave propagation in the lossless (collisionless) limit, and concentrate on the properties of normal modes in the Faraday (q parallel B₀) and Voigt (q perpendicular B₀) geometries. Essential features of the wave interaction with the medium are conveniently set forth in `contour maps' which display zeroes and infinities of the lossless dielectric constants, indicating resonances, dielectric anomalies and black-out regions for each mode of propagation over a wide range of frequencies and fields. Losses are then explicitly incorporated into the dielectric tensor, and their effect discussed in some detail. A number of experimental examples associated with the single band model are presented, including free-carrier absorption, cyclotron resonance, Faraday and Voigt effects, helicon waves, magnetoplasma reflection and small-particle effects.

The presentation is subsequently generalized to more complicated systems. The dielectric tensor is developed for a multiple-carrier plasma and for anisotropic bands. A variety of new effects is seen to arise, including hybrid resonances, tilted-orbit resonances and Alfvén wave propagation. `Contour maps' of appropriate lossless dielectric constants are again found convenient in discussing these new features. Effects of spatial dispersion (nonlocal phenomena) and of orbital quantization on the high-frequency response of a free-carrier system are then considered. The contribution of the polar lattice, which gives rise to a vast array of coupled magnetoplasma-phonon modes, is finally examined.

A further elaboration of certain topics arising in this review is presented in an appendix, including a detailed discussion of electron dynamics, the `polariton' formalism, fundamentals of Kramers-Kronig analysis and magneto-optics of birefringent media.