Radiation physics of the 21st century, which combines the special physical properties of materials and objects (nano-objects, fractals, and others) with a highly nonequilibrium state, demonstrates many unusual nonlinear effects and their interpretation. This is especially evident in the case of high-intensity irradiation of different natures and a wide energy spectrum. Taking into account five different channels of energy transfer from radiation to matter (elastic scattering, ionization, heat release, elastic waves, and shock waves) makes it challenging to manage new unusual combinations of radiation response, the study of which at the present stage is possible using the concept of “complexity.” Among the various characteristics of irradiated objects, the hierarchy of their structure takes a special role, which is fundamental for objects of both inorganic and living nature. The peculiarity of including objects of a hierarchical structure in the analysis of radiation-induced effects leads to a new situation: the involvement of the ideas of cybernetics in radiation physics. Here, new issues arise concerning the relationship between radiation and information, in particular, the effect of the entire range of radiation parameters (energy, intensity, 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 to these problems requires the use of both new theoretical approaches and the modification of conventional schemes in relation to elementary acts of atomic rearrangements, such as kinetics and approaches to revealing the mechanisms of radiation-induced effects. These questions are formulated, and a certain solution has been obtained in relation to objects of inorganic and living nature. © 2023, Pleiades Publishing, Ltd.