We review a new, rapidly developing field of all-dielectric nanophotonics
which allows to control both magnetic and electric response of structured
matter by engineering the Mie resonances in high-index dielectric
nanoparticles. We discuss optical properties of such dielectric nanoparticles,
methods of their fabrication, and also recent advances in all-dielectric
metadevices including couple-resonator dielectric waveguides, nanoantennas, and
metasurfaces
