Metasurface is an ultrathin planar device composed of artificial microstructures, which can be used to manipulate the amplitude, phase, and polarization of electromagnetic (EM) waves. Metasurface has the advantages of small volume, light weight, highly integrated, flexible manipulation of EM waves, so it plays an important role in the field of EM wave spectrum and wavefront modulation. In this paper, the research progresses of metasurface for wavefront modulation in the terahertz (THz) waveband were reviewed. The amplitude and phase modulation mechanisms of three kinds of microstructure units in the metasurface, including the microstructure based on Pancharatnam-Berry (PB) phase, localized surface plasmon resonance (LSPR) and Mie resonance were summarized, and the methods for realizing metasurface with high efficiency were discussed. After that, the pure phase and complex amplitude modulation methods for designing the wavefront modulation metasurface were introduced. Specifically, the typical functions, including single function and multifunction and tunable function, of the wavefront modulation metasurfaces in the THz waveband were reviewed. In the early research, metasurfaces were used to realize beam focusing, beam deflection, holographic imaging, and special beam generation such as vortex beam, Airy beam, and Lorentz beam in the THz region. In order to improve the utilization of a THz component, multifunctional metasurfaces, such as metasurfaces with polarization and wavelength multiplexing were proposed. With the requirement of dynamic control of the THz wavefront, some active metasurfaces were proposed and demonstrated. There were two kinds of active metasurfaces. One of the active metasurfaces was formed by combining the metasurface with semiconductor or phase transition materials, and the other was the all-optical metasurface formed by a silicon wafer with pump beam. The all-optical metasurfaces can be reused without reprocessing. The THz wavefront can be modulated dynamically by adjusting the image of the metasurface projected on the silicon wafer. Thus, the all-optical metasurface had the ability to dynamically control the beam steering and focusing, and it can be applied in THz communication, THz radar and other fields. At the end, the development trend and application prospects of the metasurfaces for wavefront modulation in the THz waveband were discussed.