Future technologies underpinning high-performance optical communications, ultrafast computations, and compact biosensing will rely on densely packed reconfigurable optical circuitry based on subwavelength optics, often called nanophotonics. For many years, plasmonics was considered as the only available platform for subwavelength optics, but the recently emerged field of Mie resonant metaphotonics provides practical alternatives for nanoscale photonic technologies by employing resonances in high-index dielectric nanoparticles and metasurfaces. In this talk I aim to introduce this recently emerged new field and discuss the physics of dielectric Mie-resonant structures governed by resonances in dielectric nanoantennas and metasurfaces. I will pay a special attention to discussing nonlinear effects such as harmonic generation from nanoantennas, nonlinear imaging with metasurfaces, and self-action effects observed in nonlinear metasurfaces.