Metasurface is an artificial material composed of a series of subwavelength structure units and has unique electromagnetic characteristics. Based on the ability of manipulating the phase, amplitude, and polarization of electromagnetic wave, various kinds of metasurfaces are designed to realize wavefront manipulations, such as beam focusing, beam steering, vector beams generating, and holographic imaging. This paper reviews the design methods of metasurfaces for wavefront modulation and evolution of the metasurfaces designed for wavefront manipulation in the terahertz (THz) region. The metasurfaces can be divided into two categories: passive and active metasurfaces. For the passive metasurfaces, the singlefunctional metasurfaces, multifunctional metasurfaces, and high diffraction efficient metasurfaces designed for various THz wavefront shaping, such as focusing, imaging, and special beams generating, are reviewed. For the active metasurfaces, the metasurfaces with fixed structure and all-optical metasurfaces without fixed structure for THz wavefront modulation are summarized. Furthermore, a comparison on the performance of different kinds of metasurfaces for THz wavefront modulation is presented and the development direction and challenges of the THz wavefront modulation metasurfaces in the future are discussed.