A critical review is presented of the theoretical and experimental research on self-focusing, and its main purposes and development trends are noted. It is indicated that the most complete definition of self-focusing, from which all its variants follow, is a decrease of the divergence (or, equivalently, an increase of the convergence) of high-power radiation in a medium. It is noted that the spatial distribution of the focusing action makes the waveguide description most complete, since it is universally known that waveguides come in a variety of cross sections, lengths, and dielectric-constant distributions, while an arbitrary radiation flux (a beam of rays) can be subdivided into self-focusing beams. The main purpose of self-focusing, namely, directed transmission of concentrated radiation and focusing the radiation into a single focus, is noted. It is shown that in practice the multifocus regime is not suitable for this purpose. It is indicated that the multifocus structure is a particular case of a previously described subdivision of a beam into beams of near-threshold power. Practical applications of self-focusing for radiation energetics, high-temperature heating of matter, control of destruction processes, acceleration of particles by a traveling focus, and others, are indicated.

@article{Askar’yan:1974,
	author = {G. A. Askar’yan},
	title = {The self-focusing effect},
	publisher = {Physics-Uspekhi},
	year = {1974},
	journal = {Phys. Usp.},
	volume = {16},
	number = {5},
	pages = {680-686},
	url = {https://ufn.ru/en/articles/1974/5/f/},
	doi = {10.1070/PU1974v016n05ABEH004130}
}