Optical spectroscopy of carbon nanotubes has become one of the methods of choice for the investigation of the fundamental physical properties of these fascinating one-dimensional systems. Depending on how a nanotube is wrapped up from a single plane of graphite (graphene) it may be semiconducting or metallic, which makes it a highly appropriate material for application in nanoelectronics.
After a general introduction into the vibrational and electronic properties of carbon nanotubes we focus on the explicit determination of chiral indices, an issue of utmost importance for the application of nanotubes. Resonant Raman scattering - a simultaneous investigation of the electronic transitions and vibrational modes - yields both the chiral index assignment and the electronic transition energy for each individual nanotube. Our assignment is based on the relation of the resonance maxima of certain vibrational modes as a function of the laser excitation energy and the inverse frequency of those modes. These vibrational modes run through the Raman spectra in ``laola''-like waves (as spectators sometimes do in a soccer stadium) and may be compared to a theoretical plot of this relationship in a so-called Kataura plot. We also present the higher excitonic transitions in the photoluminescence spectra, an issue of much recent interest in the optical work on nanotubes.