This chapter includes both experimental and theoretical results on Raman spectroscopy of carbon nanotubes. Raman-scattering measurements are reported on the effect of using different kinds of carbon nanotube samples. Resonance Raman profiles (intensity vs. excitation energy), associated with different types of carbon nanotubes have been obtained from a quasicontinuous change of the excitation energy. Experimental plots of optical transition energies as a function of the nanotube diameter have been obtained from the experiments and can be directly compared with theoretical calculations. In the theory part, we have investigated the Raman spectra of the first-order Raman process in terms of excitonic states and their interaction with photons and phonons. We compare these results with former theoretical results obtained on the basis of the electron-hole pair picture. We show that the Raman intensity shows a unique chiral-angle and diameter dependence for single-wall carbon nanotubes.