Light manipulation by means of nanoscale structures has attracted enormous interest due to its impact on modern photonic technologies. Nanoscale objects not only might facilitate the integration of various linear and nonlinear functionalities in nanophotonic circuits, but they also allow to replace bulky components by tremendously improving miniaturization [1]. Recently, high-refractive-index nanostructures with large intrinsic optical nonlinearities have been demonstrated to provide a powerful and competitive alternative to nonlinear nanoplasmonics [2,3]. Fascinating results have been predicted and obtained for second- [4–10] and third- [11–13] harmonic generation from dielectric nanoparticles; these results set their roots in the unique linear optical properties of nonmetallic nanoresonators, which have recently attracted incredible attention for the possibility that they offer to simultaneously engineer electric and magnetic resonances [14–17]. Without a doubt, we can say that all-dielectric nanoantennas and metasurfaces are very promising building blocks that are promoting a paradigm shift for nonlinear optics at the nanoscale [18].