Metamaterial is a kind of material/structure that is artificially designed and has exceptional electromagnetic properties and/or other physical properties, not found in nature. A class of electromagnetic metamaterial with only one or a few layers of periodic or aperiodic arranged cell structures in the direction of electromagnetic waves propagation can be referred to as a metasurface. Metasurface can be considered as a two-dimensional representation of metamaterial and can realize the controlling of the amplitude, phase, and polarization state/direction of the incident electromagnetic wave. According to the novel electromagnetic characteristics of metasurface and its big advantages, a series of new planar devices and systems based on metasurface can be developed. The goal of this review article is firstly to provide introductions for basic metasurface, its significance properties, and application principles. Meanwhile, the main research progresses of regular metasurfaces and the newly developed reconfigurable metasurfaces are analyzed, focusing on the types of amplitude modulation, phase modulation, polarization modulation, and multidimensional modulation. Finally, the research significances of metasurface development trend and important engineering practical applications are analyzed in the end.