Metasurfaces, a kind of two-dimensional metamaterials, can flexibly manipulate the phase, amplitude, polarization and other parameters of light waves on a flat plane. Phase gradient metasurfaces can defy the classical laws of refraction and reflection so that light field manipulation no longer needs to rely on curved optical elements, while an effective way can be provided to realize an integrated multifunctional planar optical system. In particular, through the coordinated regulation of the geometric phase and propagation phase, composite-phase metasurfaces can efficiently solve the basic drawbacks of single functionality, limited bandwidth, poor tunability, and so forth. In this work, we review the principle and method of composite-phase manipulation, and the typical applications and characteristics of composite-phase metasurfaces. Finally, we summarize and look ahead to future research directions.