Although QMC methods can be used to obtain some information on excited states, they are primarliy ground state methods. A more general approach to excited state properties is provided by many-body perturbation theory. I am involved in a long-term collaboration with Rex Godby (University of York) on applying many-body perturbation theory to solids within the GW approximation. These methods were specifically designed to calculate excited state properties such as the single particle spectral functions measured in photoemission and inverse photoemission experiments. The GW method is based on a perturbation expansion in the screened Coulomb interaction, and will therefore remain largely restricted to the study of conventional Fermi liquids, where it is currently the preeminent method for obtaining accurate results for excited state properties. The newly-developed space-time method, in which the many-body quantities are represented in real space and imaginary time, now allows the calculation of the full non-local, dynamic self-energy, and the full Green's function and spectral function, for highly complicated unit cells.