The use of Raman spectroscopy to reveal the remarkable structure and properties of carbon nanotubes is briefly reviewed. Particular emphasis is given to the fact that a nanotube can be semiconducting or metallic depending on its diameter dt and chirality θ, and how Raman spectroscopy at the single nanotube level reveals such information. Some of the implications of the unusual properties of carbon nanotubes are summarized. It is shown how the vibrational spectra of one tiny tube, only about 1 nm in diameter, can be observed experimentally. Raman spectroscopy normally measures vibrational frequencies. What is unique about carbon nanotubes is that for this one-dimensional system, resonance Raman spectroscopy (RRS) also determines, in addition, the geometrical structure of the resonant nanotube, that is its diameter and chirality. Some of the recent advances in single nanotube spectroscopy are briefly discussed. The use of RRS for characterizing carbon nanotube samples is also discussed. The connection between Raman spectroscopy and photoluminescence for studying carbon nanotubes is mentioned. Some of the current research challenges facing the field are briefly summarized.