In this paper, we present recent results obtained on single-walled carbon nanotubes (SWNTs) and carbon nanotube/conjugated polymer composites by using resonant Raman scattering and Surface Enhanced Raman Scattering (SERS). Besides the characterization of these materials, we report on peculiar properties observed in the anti-Stokes Raman branch of the Raman spectra. They consist in an abnormal anti-Stokes Raman emission which is explained by a mechanism reminiscent of a Coherent anti-Stokes Raman Scattering (CARS) emission. It results from a wave mixing process between the incident laser light and Stokes Raman light, generated by the SERS mechanism. In a parallel way, we have investigated in details the resonance effects which also induce anomalies in the anti-Stokes/Stokes intensity ratios, as a function of several parameters including the observation temperature, the environmental conditions, the dilution in solvents, etc. Studies extended to composites based on carbon nanotubes and conjugated polymers reveal also interesting properties. In the case of poly(bithiophene) (PBTh), one observes a strong amplification of the 1450 cm(-1) Raman line in the anti-Stokes branch, generated by the plasmon excitation of metallic tubes. This phenomenon occurs in several other conjugated polymers such as PEDOT and PPV for modes located around 1500 cm(-1). The role of metallic SWNTs is discussed. Finally, an anti-Stokes luminescence excited in the low energy tail of the absorption band of PPV and PPV/SWNTs composites has even been observed for the first time, explained through a phonon-energy up-conversion mechanism.