The constitutive relations close the electromagnetic propagation problem by specifying the coupling of the light field to the material. The coupling assumed here is the dipole interaction and the nature of the constitutive relation depends on whether the dipole interaction is nonresonant or resonant. In general the constitutive relations are very difficult to establish theoretically although formal quantum mechanical expressions can be written down readily. In this section we will elaborate on both nonresonant and resonant interactions with an external light field. For transparent dielectrics, the induced polarization field can be expanded as a power series in powers of the electric field. If the electric field becomes sufficiently intense, laser-induced-breakdown (LIB) can occur through the generation of a plasma. The latter can be generated via two nonlinear mechanisms, avalanche photoionization or multiphoton ionization. The simplest resonant absorption interaction occurs for an optical pulse incident on a two-level absorber. This is described by the two-level Maxwell-Bloch equations below. We will close with a discussion of a much more complex resonant coupling process, namely, the interaction of an optical pulse with a two-band semiconductor. Here, many-body microscopic interactions play an important role and the problem proves extremely challenging theoretically.