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The survey is devoted to the asymptotic theory of electro-magnetic waves in dispersive media with variable parameters. General questions of the space-time geometric-optics method are considered in Section I. The peculiarities of the material equations for weakly nonstationary dispersive media are discussed in Section II. Numerous physical problems which admit analytical solutions by the geometrical-optics method are considered in Section III (modulated-wave propagation in nondispersive media) and in Section IV (modulated-wave propagation in dispersive media); here, we describe short wavetrain propagation, wave phenomena in media with traveling parameters, compression of frequency-modulated pulses, and other problems. In Section V, the refraction and polarization phenomena arising in nonuniformly moving media are studied. Section VI deals with some problems lying beyond the frames of the geometrical optics (the behavior of the electromagnetic field in the vicinity of space-time caustics, quasi-optical description of wave packet propagation). Finally, in Section VII, some new statistical phenomena are investigated for waves propagating in nonstationary random media.