  Scattering of electromagnetic waves by subwavelength objects is accompanied
by the excitation of electric and magnetic Mie resonances, that may modify
substantially the scattering intensity and radiation pattern. Scattered fields
can be decomposed into electric and magnetic multipoles, and the magnetic
multipoles define magnetic response of structured materials underpinning the
new field of all-dielectric resonant meta-optics. Here we review the recent
developments in meta-optics and nanophotonics, and demonstrate that the Mie
resonances can play a crucial role offering novel ways for the enhancement of
many optical effects near magnetic and electric multipolar resonances, as well
as driving a variety of interference phenomena which govern recently discovered
novel effects in nanophotonics. We further discuss the frontiers of
all-dielectric meta-optics for flexible and advanced control of light with full
phase and amplitude engineering, including nonlinear nanophotonics, anapole
nanolasers, quantum tomography, and topological photonics.
