Radiation physics of the 21st century, which combines the special physical properties of materials and objects (nanoobjects, fractals, and others) with strong non-equilibrium, demonstrates many unusual nonlinear effects and their interpretation. This is especially evident in the case of high-intensity irradiation of various natures with a wide energy spectrum. Taking into account five different channels for the transfer of radiation energy to matter (elastic scattering, ionization, heat release, elastic and shock waves) makes it difficult to see the number of new unusual combinations of the radiation responses, the study of which at the present stage, apparently, is possible using the concept of “complexity”. Among the various characteristics of irradiated objects, a special role is played by the hierarchy of their structure, which is fundamentally important for objects of both inanimate and living nature. The peculiarity of including objects of a hierarchical structure in the analysis of radiation effects leads to a new situation – the involvement of the ideas of cybernetics in radiation physics. Questions of a new type arise concerning the relationship between radiation and information, in particular, the influence of the entire variety of radiation parameters (energy, intensity, and dose) on the transfer of information from the lower platform of hierarchical structures to higher ones and its compression at the same time. The solution of these problems requires the use of both new theoretical approaches and the modification of traditional schemes in relation to the elementary acts of atomic rearrangements, such as kinetics and approaches to revealing the mechanisms of radiation effects. This range of questions has been formulated, and a certain solution has been obtained in relation to objects of inanimate and living nature.