By taking ordinary materials and rearranging them into complex shapes on the same scale as the wavelength of light, it is well known that one can drastically enhance the interactions between light and matter, from resonant absorption to spontaneous emission to surface-enhanced Raman scattering. In this talk, we will present a recent theoretical technique that reveals upper limits to such enhancement for a given material, regardless of the geometric shape. These theoretical bounds provide guidance to the engineering design of new devices, whether by intuitive hand designs or massive computational geometry optimization. In some cases, we find that simple known structures are nearly optimal, but in other cases (such as Raman sensing) there appears to be enormous room for improvement attainable by new geometries. Moreover, the upper limits derive from remarkably simple principles — energy conservation and the optical theorem — that allow them to be generalized to a wide range of phenomena. Already, we have found new upper limits to absorption, scattering, spontaneous emission, thermal radiation, Cherenkov radiation, and Raman scattering, as well as figures of merit allowing rapid comparison of optical materials over different bandwidths.