Two-dimensional metasurfaces are widely focused on for their ability for flexible light manipulation (phase, amplitude, polarization) over sub-wavelength propagation distances. Most of the metasurfaces can be divided into two categories by the material type of unit structure, i.e., plasmonic metasurfaces and dielectric metasurfaces. For plasmonic metasurfaces, they are made on the basis of metallic meta-atoms whose optical responses are driven by the plasmon resonances supported by metallic particles. For dielectric metasurfaces, the unit structure is constructed with high refractive index dielectric resonators, such as silicon, germanium or tellurium, which can support electric and magnetic dipole responses based on Mie resonances. The responses of plasmonic and dielectric metasurfaces are all relevant to the characteristics of unit structure, such as dimensions and materials. One can manipulate the electromagnetic field of light wave scattered by the metasurfaces through designing the dimension parameters of each unit structure in the metasurfaces. In this review article, we give a brief overview of our recent progress in plasmonic and dielectric metasurface-assisted nanophotonic devices and their design, fabrication and applications, including the metasurface-based broadband and the selective generation of orbital angular momentum (OAM) carrying vector beams, N-fold OAM multicasting using a V-shaped antenna array, a metasurface on conventional optical fiber facet for linearly-polarized mode (LP 11 ) generation, graphene split-ring metasurface-assisted terahertz coherent perfect absorption, OAM beam generation using a nanophotonic dielectric metasurface array, as well as Bessel beam generation and OAM multicasting using a dielectric metasurface array. It is believed that metasurface-based nanophotonic devices are one of the devices with the most potential applied in various fields, such as beam steering, spatial light modulator, nanoscale-resolution imaging, sensing, quantum optics devices and even optical communication networks.