The optical properties of single-wall carbon nanotubes (SWNTs) are dominated by the excitonic character of the transitions even at room temperature. The very peculiar properties of these excitons arise from both the one-dimensional (1D) nature of carbon nanotubes and from the electronic properties of graphene from which nanotubes are made. We first propose a brief qualitative review of the structure of the excitonic manifold and emphasize the role of dark states. We describe recent experimental investigations of this excitonic structure by means of temperature dependent PL measurements. We investigate the case of upper sub-bands and show that high-order optical transitions remain excitonic for large diameter nanotubes. A careful investigation of Rayleigh scattering spectra at the single nanotube level reveals clear exciton-phonon side-bands and Lorentzian line profiles for all semi-conducting nanotubes. In contrast, metallic nanotubes show an ambivalent behavior which is related to the reduced excitonic binding energy. Schematic of the exciton manifold in single-wall carbon nanotubes. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.