A systematic theory of first-order electrodynamic relativistic effects in media moving with a spatially nonuniform velocity is presented. A geometrical optics approach is developed and used to calculate the bending of rays and the change of polarization characteristics of radiation propagating through a continuous medium moving with a nonuniform velocity. Nonreciprocal (i.e., propagation direction-dependent) waveguides and lenses in media moving with a transversely nonuniform velocity are demonstrated. Radiation scattering (diffraction) by localized velocity nonuniformities is studied. Peculiarities of propagation of short-wave (X-ray) radiation in a moving medium are discussed, and some prospects for experimentation are reviewed.