Carbon-based semiconductors are being widely investigated for applications in future optoelectronic devices. Organic light-emitting diodes have already seen commercial success, while significant progress is being made in the areas of organic photovoltaics and transistor devices. There is currently intense interest in graphene and its derivatives as electronic materials with ultrahigh intrinsic charge carrier mobility. The photophysics of carbon nanostructures is, however, remarkably different from that of conventional inorganic semiconductors, because of the strong Coulomb interactions among the -electrons of the former. Textbook single-particle concepts do not apply to carbonbased materials, and there is a strong need for the development of new theoretical concepts. This theoretical talk will focus on the consequences of strong electron-electron interactions on the behavior of two classes of materials: semiconducting single-walled carbon nanotubes and graphene nanofragments. Detailed comparisons to experiments, some performed by the speaker’s collaborators, will be made. The emphasis is on physical understanding and not the details of calculations. The talk is specifically directed to graduate students.