The primary reactions of purple bacterial photosynthesis take place within two well characterized pigment-protein complexes, the core Reaction Center-Light Harvesting 1 (RC-LH1) complex and the more peripheral Light Harvesting 2 (LH2) complex. These antenna complexes serve to absorb incident solar radiation and to transfer it to the reaction-centers, where it is used to 'power' the photosynthetic redox reaction. This review provides an overview of how the character of the electronically excited states of these pigment-protein complexes are determined by quantum mechanics and how the respective spectral signatures can be observed by single-molecule spectroscopy.