Metasurfaces can be designed for the spatial transformation of wavefronts. Research on the two-dimensional periodic optical metasurfaces mainly focuses on controlling the wavefront of light propagating in free space. In recent years, researchers have designed a series of one-dimensional on-chip metasurfaces to control the degree of freedom in on-chip optical signal transmission and further realize a small-size, broadband, and low-loss integrated photonic computing chip. This article summarized the related work on on-chip nanophotonic devices based on dielectric metasurfaces. To be specific, we reviewed and discussed the physical mechanisms, implementation methods, and applications of on-chip metasurfaces in integrated nanophotonic devices. Besides, we undertook a general review of the remaining challenges and proposed possible development directions that require further study for the application of on-chip metasurfaces to integrated nanophotonic devices.