The theoretical concepts of Raman scattering by free current carriers in semiconductors and metals are reviewed. Various elementary excitations are discussed as the sources of the light-scattering fluctuations: one-particle charge-density fluctuations and plasmons, spin-density fluctuations, and fluctuations of the density of electron energy and momentum. These elementary excitations are common to different solids: metals, semimetals, semiconductors, and superconductors. As an adequate mathematical apparatus that reflects the unitary nature of the Raman spectra of these elementary excitations in various solids, a macroscopic approach to describing their relaxation is proposed. In this approach one distinguishes two mechanisms of relaxation: the diffusion mechanism, in which relaxation occurs via diffusional fluxes of varying nature, and the Mandel'shtam–Leontovich mechanism, in which adiabatic relaxation of the light-scattering fluctuations occurs. In multivalley semiconductors these mechanisms coexist, giving an additive contribution to the reciprocal relaxation time of the fluctuations: in single-valley semiconductors, metals, and superconductors, one of these mechanisms is realized, depending on the details of the electron band structure. Here the correlation function that determines the Raman cross section satisfies the same kinetic or diffusional equation as the fluctuating quantity itself. As technical applications, the possibility is pointed out of contact-free determination of the parameters of the electronic spectrum of semiconductors, metals, semiconductor superlattices, and superconductors.