Shaping light with metamaterials: From nonlinear response to all-dielectric nanophotonics

We review the recent progress in the field of metamaterials-artificial structures for controlling electromagnetic waves from microwaves to visible frequencies. The topics discussed will include optically-induced magnetic response, the effects of structure geometry, nonlinear properties originating from electric and magnetic response, emission control, and hyperbolic metamaterials. A special attention will be paid to the recently emerged new field of all-dielectric metamaterials and nanophotonics.