  In this work, we investigate mathematical models for electromagnetic wave
propagation in dispersive isotropic media. We emphasize the link between
physical requirements and mathematical properties of the models. A particular
attention is devoted to the notion of non-dissipativity and passivity. We
consider successively the case of so-called local media and general passive
media. The models are studied through energy techniques, spectral theory and
dispersion analysis of plane waves. For making the article self-contained, we
provide in appendix some useful mathematical background.
