Single-walled carbon nanotubes (SWNTs) are fascinating materials to study one-dimensional photophysics. Their optical properties are strongly affected by strong Coulomb interactions and are determined by "excitons" which represent the quantum of polarization in non-metallic solids. In this thesis dissertation we have experimentally investigated both the structure and the dynamics of excitons in non-metallic SWNTs. In particular, we have performed micro-photoluminescence spectroscopy of individual semiconducting SWNTs at low temperature to study their intrinsic optical properties and investigate the excitonic fine structure. Using magnetic field parallel to the tube axis we were able to directly observe theoretically predicted dark states for the first time in SWNTs. In addition, we found that the inter-valley and exchange energy, which determines the energy separation between the dark and the bright state, to be very sensitive to the surrounding environment of the nanotube. We have also studied the temperature dependent lineshape of SWNT photoluminescence in order to gain insight into the dynamics of exciton-phonon interaction, finding evidence for acoustic phonon scattering. For the rest of this thesis dissertation, we have developed a model based on reaction-diffusion processes to theoretically explain the observation of photoluminescence saturation in SWNTs. Our model shows that efficient exciton-exciton annihilation under high pumping conditions can explain this observed behavior quantitatively.