  Bound states in the continuum provide a remarkable example of how a simple
problem solved about a century ago in quantum mechanics can drive the research
on a whole spectrum of resonant phenomena in wave physics. Due to their huge
radiative lifetime, bound states in the continuum have found multiple
applications in various areas of physics devoted to wave processes, including
hydrodynamics, atomic physics, and acoustics. In this review paper, we present
a comprehensive description of bound states in the continuum and related
effects, focusing mainly on photonic dielectric structures. We review the
history of this area, basic physical mechanisms in the formation of bound
states in the continuum, and specific examples of structures supporting such
states. We also discuss their possible applications in optics, photonics, and
radiophysics.
