Metasurfaces, the equivalent two-dimensional (2D) metamaterials, are thin-film functional devices constructed by subwavelength structures. Abrupt phase changes can be obtained in the planar metasurface structures over the subwavelength scale, which provide a new avenue to enable a variety of applications, including large scale planar imaging, electromagnetic virtual shaping and holographic display with large field of view. The arbitrary modulation abilities of phase, amplitude and polarization at the subwavelength scale, also the light weight, low loss, integratable and conformable design make the metasurfaces very attractive, compared to the traditional optical devices. In this paper, we review the mechanisms of the phase modulation and classify the metasurfaces based on them. The properties and the applications of each type of metasurfaces are also detailedly discussed. The challenges faced by metasurfaces and the areas which need to be further extended are also summarized.