  The review presents an analysis and generalization of classical and most
modern approaches to the description and development of operation of open
optical nanoresonators, that is, resonators all sizes of which are smaller than
the resonant wavelength of radiation in a vacuum. Particular attention is paid
to the physics of such phenomena as bound states in a continuum, anapole
states, supercavity modes, and perfect nonradiating modes with extremely high
quality factors and localizations of electromagnetic fields. An analysis of the
optical properties of natural oscillations in nanoresonators made of
metamaterials is also presented in the review. The effects considered in this
review, besides being of fundamental import can also find applications in the
development of optical nanoantennas, nanolasers, biosensors, photovoltaic
devices, and nonlinear nanophotonics.
