Classical MD simulation is an excellent tool for refining our general physical understanding of interfacial electrostatic properties. In particular, simulations enable direct evaluation of the assumptions that underlie standard theoretical models. The ubiquitous assumption that solvent is a simple dielectric continuum is not generally applicable at interfaces. At the interface, solvent dielectric is both anisotropic (different in parallel and perpendicular directions) and spatially varying. Alternately, the solvent dielectric response can be represented as an explicit finite width contribution to the charge density field, resulting in significant deviations from Gouy-Chapman-like theories.