Raman spectroscopy has historically played an important role in the structural characterization of graphitic materials, in particular providing valuable information about defects, stacking of the graphene layers and the finite sizes of the crystallites parallel and perpendicular to the hexagonal axis. Here we review the defect-induced Raman spectra of graphitic materials from both experimental and theoretical standpoints and we present recent Raman results on nanographites and graphenes. The disorder-induced D and D' Raman features, as well as the G'-band (the overtone of the D-band which is always observed in defect-free samples), are discussed in terms of the double-resonance (DR) Raman process, involving phonons within the interior of the 1st Brillouin zone of graphite and defects. In this review, experimental results for the D, D' and G' bands obtained with different laser lines, and in samples with different crystallite sizes and different types of defects are presented and discussed. We also present recent advances that made possible the development of Raman scattering as a tool for very accurate structural analysis of nano-graphite, with the establishment of an empirical formula for the in- and out-of-plane crystalline size and even fancier Raman-based information, such as for the atomic structure at graphite edges, and the identification of single versus multi-graphene layers. Once established, this knowledge provides a powerful machinery to understand newer forms of sp(2) carbon materials, such as the recently developed pitch-based graphitic foams. Results for the calculated Raman intensity of the disorder-induced D-band in graphitic materials as a function of both the excitation laser energy (E(laser)) and the in-plane size (L(a)) of nano-graphites are presented and compared with experimental results. The status of this research area is assessed, and opportunities for future work are identified.