  Nonradiating sources are nontrivial charge-current distributions that do not
generate fields outside the source domain. The pursuit of their possible
existence has fascinated several generations of physicists and triggered
developments in various branches of science ranging from medical imaging to
dark matter. Recently, one of the most fundamental types of nonradiating
sources, named anapole states, has been realized in nanophotonics regime and
soon spurred considerable research efforts and widespread interest. A series of
astounding advances have been achieved within a very short period of time,
uncovering the great potential of anapole states in many aspects such as
lasing, sensing, metamaterials, and nonlinear optics. In this review, we
provide a detailed account of anapole states in nanophotonics research,
encompassing their basic concepts, historical origins, and new physical
effects. We discuss the recent research frontiers in understanding and
employing optical anapoles and provide an outlook for this vibrant field of
research.
