  The original Kerker effect was introduced for a hypothetical magnetic sphere,
and initially it did not attract much attention due to a lack of magnetic
materials required. Rejuvenated by the recent explosive development of the
field of metamaterials and especially its core concept of optically-induced
artificial magnetism, the Kerker effect has gained an unprecedented impetus and
rapidly pervaded different branches of nanophotonics. At the same time, the
concept behind the effect itself has also been significantly expanded and
generalized. Here we review the physics and various manifestations of the
generalized Kerker effects, including the progress in the emerging field of
meta-optics that focuses on interferences of electromagnetic multipoles of
different orders and origins. We discuss not only the scattering by individual
particles and particle clusters, but also the manipulation of reflection,
transmission, diffraction, and absorption for metalattices and metasurfaces,
revealing how various optical phenomena observed recently are all ubiquitously
related to the Kerker's concept.
