A review is presented on the observation of the resonant Raman spectra from one isolated single wall carbon nanotube, focusing on the important structural information that is provided by single nanotube spectroscopy including the (n, m) determination of the individual tubes. The special sensitivity of the radial breathing mode to the (n, m) determination is emphasized, and the corroboration of this (n, m) assignment by diameter- and chirality-dependent phenomena in other Raman modes, such as the G-band, D-band, and G'-band features is also discussed. The significance of single nanotube spectroscopy for future nanotube research in general is briefly reviewed.