High energy nuclear physics has important purely scientific value and applied value. Statistical methods of calculation based on the intranuclear cascade model permit agreement to be obtained with the known experimental data over the entire energy range above several tens of MeV. For energies T $\gtrsim$ 3--5 BeV it is necessary to take into account the change in the density of intranuclear matter with development of the cascade of particles inside the target-nucleus; in the transition to the very high energy region it is necessary to take into account also many-particle interactions in which several fast particles collide with one nucleon at the same time. The methods of calculation are discussed briefly, and the results and the difficulties encountered in the calculations are considered. Special attention is devoted to interactions with targets of the light nuclei d, t, He$^3$, and He$^4$. Scale invariance of the interactions of high-energy particles and nuclei is discussed.