The notion of the radiative strength function was introduced for the description of gamma transitions from highly excited states in a wide energy range near the neutron separation energy [1]. This quantity is necessary for the calculation of all characteristics of radiative processes in nuclei, in particular, the cross sections for radiative capture of a neutron, which is one of the most important reactions in processes of nucleosynthesis and in the calculations of nuclear and nuclear fusion reactors. The generalized radiative strength function, which involves transitions between excited states, is usually used. In this case, the use of the radiative strength function in the calculation of cross sections for radiative processes is based on the Brink-Axel hypothesis [2,3]. According to this hypothesis, the giant dipole resonance (GDR) can be constructed on any excited state and its properties are independent of the nature of this state. Within this hypothesis, which currently is a commonly accepted, mainly justified approximation, the radiative strength function is simply related to the photoabsorption cross section (see below) and to the problems of the pygmy dipole resonance (PDR) (see [4]).The problems of the PDR have attracted significant attention of researchers in "pure" nuclear physics and of specialists in nuclear data in recent years [5][6][7]. This resonance is located in the low energy tail of the GDR, i.e., in a wide region near the nucleon separa tion energy. Although it usually exhausts 1-2% of the Thomas-Reiche-Kuhn sum rule, its role in radiative nuclear processes is very significant [8]. We also emphasize that the characteristics of the PDR in nuclei with a low neutron separation energy (below 3-4 MeV) are strongly different and, consequently, phe nomenological systematics based on data obtained for stable nuclei with a normal separation energy near 8 MeV are inappropriate. In this sense, the phenome nological description is not predictive. For this reason, self consistent microscopic approaches are actively developed. They are much more predictive and pre tend to describe both ground and excited states of all nuclei, except for the lightest, with a set of a few (about ten) universal parameters describing either Skyrme forces or the energy functional [5,6,8].The microscopic nature of the radiative strength function, which is the most important characteristic neces sary for the description of nuclear reactions involving gamma ray photons both in astrophysics and in the the ory of nuclear reactors, has been discussed. It has been shown that, in contrast to phenomenological approaches based on various modifications of the Lorentzian dependence for this function, the microscopic approach gives structures that are due to the effects both within the standard random phase approximation and of coupling with low lying collective excitations (phonons), i.e., beyond the standard random phase approximation. Microscopic calculations of the strength function for several Sn and Ni isotopes have been performed wi...