We review a number of the important results of the theory of radiation transport of resonance radiation obtained mainly during the past decade. Situations are stressed in which the traditional hypothesis of complete frequency redistribution of quanta is not fulfilled in the process of reemission. A quite general approach to the problem of radiation transport is presented that assumes small frequency shifts in the scattering event. Results are presented pertaining to the rate of deexcitation in Doppler, Stark, and natural mechanisms of line broadening. The transport of polarized radiation is discussed, including the application to experiments on interference of atomic states (the Hanle effect, etc.). The problem is discussed of transport of high-intensity radiation, in particular as applied to the problem of radiation trapping in lines of hydrogen-like ions. The connection is discussed of the physical mechanisms of radiation transport in spectral lines and in a recombination continuum.