Frequency conversions, such as second harmonic generation (SHG), third harmonic generation (THG), high harmonic generation (HHG), and wave mixing, are typical processes in nonlinear optics, which have a wide range of applications in new light sources, bioimaging and sensing, quantum optics, and holography. To engineer and manipulate these nonlinear optical processes, metasurfaces and nanophotonic structures have been introduced, which have been successfully demonstrated as powerful tools to tailor the key features of light and excite the extraordinary phenomena in linear optics. In this review, we highlight the recent progress on frequency conversion in plasmonic metasurfaces, all-dielectric metasurfaces as well as other nanophotonic structures, ranging from SHG, THG to HHG and wave mixing. The origin of optical nonlinearity and its coupling with subwavelength resonators are discussed, which fundamentally determine the conversion efficiency and functionality. Finally, we summarize the challenges that nonlinear metasurfaces and nanophotonics now face and offer an outlook on further development and application potential.