The present state of the general theory of response functions of material media, describing the universal properties of these functions that characterize all types of medium, is surveyed. Topics covered include recent results on the range of admissible values of static permeability, the form of the Landau functional for the electrodynamic ordering of a medium, and the electrodynamics of a medium interacting with a magnetic monopole. Applications to high-temperature superconductivity, anomalous diamagnetism, and monopole detection are discussed.