No other known material comes closer to an ideal one-dimensional system than single-wall carbon nanotubes. In this dissertation, we explore the fascinating new physics characterizing these new nanostructures. After a comprehensive and accessible introduction to the electronic and optical properties of carbon nanotubes, we present our major experimental result: at low-temperature, carbon nanotubes can act as perfect single photon sources. This observation has catapulted nanotubes to a promising candidate for the generation of tunable single photons in quantum information applications. We then investigate the interaction of localized optical excitations with the mechanical vibrations of the nanotube. Here again, the low-dimensionality of the system yields to dramatic effects with no analog in bulk materials. Motivated by the unique properties of carbon nanostructures, we also present a proposal for all-optical spin manipulation in nanotubes and explore the possibility of optomechanical cooling of a nanotube resonator to the quantum ground state. This book brings the reader on a journey through the latest developments in quantum optics with carbon nanostructures.