For twenty or more years, it has been possible to perform computations of material-specific ground state properties of solids, liquids, and molecules which agree very well with experiments. These calculations make use of theories in which the many-electron problem is replaced with an effective one-particle (mean field) problem. In the last decade it has become possible to perform calculations of low-lying excited states relevant for the accurate computation of various spectra such as photoemission and optical absorption. The theories underlying these computations are based on perturbation theory (often low order) in the screened electron-electron interaction, and seem to work very well for band insulators and metals. In this talk, I review the history of these developments, describe the basic content of these theories, and provide a host of examples of their application to materials physics. In the end, I highlight what I view to be the major challenges facing the field of excited state electronic structure theory at the present time.