While the Jaynes-Cummings and Tavis-Cummings models discussed in the Introduction provide an intuitive understanding of light-matter interactions, these simplified models break down for many systems that cannot be thought of as two-level systems or have permanent dipole. For most molecular systems, a more rigorous framework is needed to provide even qualitatively accurate results. With this in mind, this section discusses the various theoretical representations that go beyond simple quantum optics models like the Jaynes-Cummings model.