Nonlinear optics is a well-established field of research that traditionally relies on the interaction of light with macroscopic nonlinear media over distances significantly greater than the wavelength of light. However, the recently emerged fields of metaphotonics, including Mie-tronics, provides a novel platform for studying nonlinear phenomena. Nonlinear subwavelength structures and metasurfaces introduce new functionalities to the field of nonlinear optics extending them beyond perturbative regimes of harmonic generation and parametric frequency conversion. Here we review the very recent advances in the rapidly developing field of nonlinear metaphotonics, emphasizing asymmetric and chiral second- and third-harmonic generation, self-action and nonperturbative nonlinear regimes, and high harmonic generation empowered by the physics of Mie resonances and optical bound states in the continuum.