In this paper, we review recent development in the theory of resonant inelastic light (Raman) scattering in one-dimensional electron systems. The particular systems we have in mind are electron doped GaAs based semiconductor quantum wire nanostructures, although the theory can be easily modified to apply to other one-dimensional systems. We compare the traditional conduction-band-based non-resonant theories with the full resonant theories including the effects of interband transitions. We find that resonance is essential in explaining the experimental data in which the single particle excitations have finite spectral weights comparable to the collective charge density excitations. Using several different theoretical models (Fermi liquid model, Luttinger liquid model, and Hubbard model) and reasonable approximations, we further demonstrate that the ubiquitously observed strong single particle excitations in the experimental Raman spectra cannot be explained by the spinless multi-spinon excitations in the Luttinger liquid description. The observability of distinct Luttinger liquid features in the Raman scattering spectroscopy is critically discussed. q