An analysis is made of the theory of the luminescence spectra of semiconductors with direct optical transitions involving recombination of nonequilbrium carriers whose energies are close to the band gap edges. The usual formulation of the theory of recombination is employed, i.e., given densities of free electrons and holes are assumed. The first part of the review is concerned with the luminescence (of the exciton, interband, impurity, or interimpurity type) of lightly doped semiconductors. Unsolved problems are noted and it is stressed particularly that the interband luminescence spectrum is governed largely by the interaction of carriers and by the mechanisms of their scattering, but in practice this has been ignored so far in the development of the theory and in the interpretation of the experimental results. The second (main) part of the review is devoted to the luminescence of heavily doped semiconductors. It is shown that the nature of the electron spectrum of such semiconductors, involving formation of density-of-states ``tails'' and broadening of the impurity levels, is manifested clearly in this case. It is stressed that the distribution of nonequilibrium carriers between localized states corresponding to a continuous spectrum is usually quite different from the quasiequilibrium distribution, i.e., it cannot be described by introduction of the quasi-Fermi level. An allowance for this circumstance makes it possible to explain a great variety of seemingly contradictory experimental data on the luminescence spectra of heavily doped semiconductors. The deviation of the carrier distribution from the quasiequilibrium case is manifested also in transient characteristics of the luminescence, and it also governs the characteristic features of radiative recombination in strongly compensated heavily doped semiconductors, which can be regarded as one of the models of amorphous semiconductors. It is pointed out in conclusion that the proposed concepts can account for the special features of the characteristics of electroluminescent structures made of heavily doped semiconductors.