In recent years, metasurface has received extensive attention in the field of classical light control, and excellent results have been obtained. At the same time, the application of metasurface in nonlinear optics and quantum optics has also attracted more and more interest. The basic principles and applications of nonlinear metasurface and quantum metasurface were introduced, and the related reports in recent years were summarized, including the harmonic generation and enhancement, the relationship between harmonic generation and symmetry, the nonlinear phase control and holography, and the generation, measurement and manipulation of entangled photon based on metasurface. Finally, the potential application of metasurface in these two fields were prospected.