The recent advent of optical metasurfaces, ultra-thin structures composed of nanoresonators facilitating strong light concentration [1–3], opens the path toward efficient frequency conversion [4–7] in a material thousand times thinner than a human hair . There is a remarkable capacity to individually shape each nanoresonator of the metasurface to spatially and spectrally control the conversion process with unprecedented nanoscale resolution, facilitating an ultimate flexibility to selectively convert, focus, and image different colors with a single metasurface. The strong enhancement of the nonlinear processes in dielectric nanoresonators is largely due to the absence of material absorption and the excitation of Mie-type bulk resonances . The highest conversion efficiency to date has been achieved employing III–V semiconductor nanostructures, such as AlGaAs which is a non-centrosymmetric material with high 148quadratic nonlinear susceptibility. In particular, second-harmonic generation efficiencies up to 10 − 4 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351269766/15d1c3e5-fab1-4d58-916e-8992bf207991/content/equ5_1.tif"/> have been recently demonstrated [8–12], six orders of magnitude higher than in plasmonics. Such capabilities can make an immense fundamental and practical impact, including the quantum state generation in nonlinear metasurfaces as we discuss in this chapter.