The motivation behind the present work is to adopt methodology from field theory and high-energy physics to crystallography. In particular, we establish a relationship between the electromagnetic sector of the Standard-Model Extension (SME) for Lorentz invariance violation and optical media. At an effective level, a broad class of anisotropic and polarization-dependent electromagnetic properties associated with crystal structures is demonstrated to be parametrized in the SME. Crystallographic and magnetic point groups provide the mathematical tools to show this correspondence. Birefringent and magnetoelectric media merit a dedicated study. Intriguing effects, which have not been described systematically in the modern literature, are rediscovered for the latter and expressed in SME language. With the setting developed at our disposal, materials with specific symmetries such as birefringent or multiferroic crystals serve as condensed-matter analogs for SME effects. It enables us to propose materials with unusual optical properties, which have not been thoroughly looked at in recent times.