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The unique nature of optical properties of single-walled carbon nanotubes (SWCNT), together with their promising potential applications, have created enormous interest towards the photophysics of SWCNT. Many aspects of carbon nanotubes originate from the electronic structure of carbon honeycomb lattice and one-dimensionality. SWCNTs exist in various chiral structures and diameters, which the optical and electrical properties are dependent on. It has been discovered that SWCNT excited states are excitonic with strong Coulomb interaction between the electron and the hole. However, many features of excitons are not yet well defined, such as absorption cross-sections, fluorescence quantum yields, exciton lifetimes, and the nature of exciton mobility. The cylindrical shape with all atoms on the surface makes SWCNTs highly sensitive to environment which is a significant factor affecting the optical properties. First part of this thesis concentrates on the temperature dependence of excitonic absorption transitions. The importance of this study lies in the complexity of environmentally induced mechanisms to alter the energy gap and shift the electronic absorption transitions as a function of temperature. The results revealed abrupt shift in the energy gap interpreted to originate from interactions with water. The second part discusses the processes occurring after absorption: exciton mobility and dynamics. By analyzing reactions between single-molecule diazonium salt and individual nanotubes, the distance travelled by exciton during its lifetime, in different surfactants and for different chiral structures was determined. The results indicate that localized excitons have diffusional motion along the nanotube axis. The large diffusion ranges obtained (160 - 340 nm) explain the sensitivity of SWCNT emission to changes in local environment. The dynamics of excitons were studied with excitation dependence measurements. Results revealed the existence of long lived states that act as quenchers of emission even at relatively low excitation intensities.