After a brief historic review the basic phenomenology and the fundamental physical process that are responsible for producing Cherenkov radiation in refractive media are explained, followed by the elementary theory of single particle Cherenkov radiation that covers the radiation yield and spectral features. Subsequently the phenomenology and theory of Cherenkov radiation in air showers are discussed, including characteristic features such as the lateral, temporal and spectral distribution of the photons, polarization aspects, the curvature of the light front and distribution substructures. The relation between the energy of the shower initiating primary and the optical observables at ground level are analyzed and the procedure to estimate the primary energy is outlined. The effects of the nature of the primary on the Cherenkov pattern, in particular of the mass if the primary is a hadron, are outlined and correlations between Cherenkov and particle observables are illuminated. Gamma ray astronomy is briefly touched and the technique of Cherenkov imaging is presented. These topics are followed by a discussion of the optical background, atmospheric light scattering, absorption and attenuation. The chapter ends with a compilation of data that cover the entire scope of experimental work, from the early stages to the present.