A general discussion is given of the properties of electromagnetic plane waves in moving isotropic and anisotropic media. This includes working out the general constitutive relations and the dispersion relation for the isotropic case. Treatment of the moving interface involves determining not only the Doppler shifts but also generalization to a moving interface of the law of reflection, Snell’s law, formula for the critical angle, Brewster’s angle, and the reflection and transmission coefficients. The latter involve generalization of the Slater impedances associated with the incident, reflected, and transmitted waves. The maximum angle of incidence in the frame moving with the interface is shown to be that which represents a flow of energy parallel to the interface.