Single-walled carbon nanotubes (SWNTs) are extremely thin cylinders of hexagonal carbon networks with diameters on the order of 1 nm. Over the past decade, optical properties of SWNTs, dominated by correlated electron-hole bound states known as excitons, have been intensively studied. The exciton photophysics of SWNTs is relevant to nearly all optical phenomena observed in SWNTs, and their detailed understanding is critical for the development of future optoelectronic devices using SWNTs. Here we review some interesting photophysics related to excitons in SWNTs, including fundamental features in optical absorption and photoluminescence spectra, effects of exciton-phonon interactions, anisotropic optical absorption and emission, effects of surrounding materials, radiative and nonradiative lifetimes, and diffusional exciton migration along SWNTs, which have been studied by continuous-wave and time-resolved optical spectroscopy. © 2013 The Royal Society of Chemistry.