Bound states in the continuum in photonic structures

Bound states in the continuum (BICs) are a striking example of how a solution to a simple problem of quantum mechanics, obtained about a century ago, can serve as an incentive to study a wide range of resonance phenomena in wave physics. Due to the giant radiative lifetime, BICs have found multiple applications in various fields of physics studying wave processes, in particular, in hydrodynamics, atomic physics, and acoustics. In this review, we present a broad view of the physics of BICs and related effects, focusing primarily on photonic dielectric structures. We consider the history of the development of BIC studies, the main physical mechanisms of their formation, and specific examples of structures that can support such states. We also discuss possible practical applications of BICs in optics, photonics, and radiophysics.