The goal of this chapter is to review the importance of excitons to single-wall carbon nanotube (SWNT) optics. We have developed the presentation for both researchers in the SWNT field who want to learn more about the unusual aspects of SWNT exciton photophysics and researchers more knowledgeable about the physics of excitons, but not about SWNT physics. Excitons in SWNTs are special because graphite has two energy bands at the Fermi energy related to time-reversal symmetry and because SWNTs are actually one dimensional. This review discusses both theoretical and experimental points of view, thus aiming to provide a summary of the most important work in the field, as well as to identify open questions.