It follows from the foregoing that the main equations for the static and complex dielectric permittivity have now been sufficiently completely formulated, allowing the permittivity to be rigorously determined with short-range interaction taken into account. In the first case, this involves the use of the Gibbs distribution, and in the second the Kubo formalism. However, although “... the development of equilibrium statistical mechanics may be regarded as complete” (from the American foreword to [14]), the reduction of the Gibbs distribution to take into account only the dipole -dipole interactions of nearest-neighbor molecules, as is done in the Kirkwood and Frohlich theories, cannot be regarded as entirely satisfactory. For such an approach, it is necessary to know the accurate structure of the molecule and the position of the nearest-neighbor molecules, which requires special investigations. In addition, other forms of interaction are omitted, and elastic polarization is not taken rigorously into account. A much more difficult problem confronts theories of nonequilibrium relaxational polarization, in that “the development of nonequilibrium statistical mechanics is much worse, since it considers considerably more difficult time-dependent problems and the fundamental question of irreversibility” (from the same foreword). In the present review it has been shown that the basic problem of the theory of nonequilibrium relaxational polarization is to find the relation between the macroscopic and molecular distribution functions and to determine the explicit form of these functions. Rigorous solution of this problem for specific materials will allow the laws governing the establishment of relaxational polarization to be determined, together with the corresponding dispersion relations. To this end, in turn, it is necessary to know the relation between the molecular relaxation function and those defects which determine the relaxational process [74].