Single and double resonances in Raman scattering are introduced and six criteria for the observation and identification of double resonances stated. The experimental situation in carbon nanotubes is reviewed in view of these criteria. The evidence for the D mode and the high-energy mode is found to be overwhelming for a double-resonance process to take place, whereas the nature of the radial breathing-mode Raman process remains undecided at this point. Consequences for the application of Raman scattering to the characterization of nanotubes are discussed.