The discovery of fullerenes in 1985 opened a completely new field of materials research. Together with the single-wall carbon nanotubes (SWCNTs) discovered later, these curved carbon networks are a playground for pure as well as applied science. We present a review of Raman spectroscopy of fullerenes, SWCNTs and composite materials. Beginning with pristine C(60), we discuss intercalated C(60) compounds and polymerized C(60), as well as higher and endohedral fullerenes. Concerning SWCNTs, we show how the diameter distribution can be obtained from the Raman spectra and how doping modifies the spectra. Finally, the Raman response of C(60) encapsulated into SWCNTs (C(60) peapods) is discussed.