Phase is an important component of optical field information. In optical microscopy imaging, most biological cells have weak light absorption. Consequently, traditional bright field microscopy cannot accurately characterize the structural characteristics of cells. Therefore, phase imaging has become an important method for non-labeled cell observations. The classic phase contrast microscope is based on the principle of interferometric imaging and typically requires large refractive prisms or complex imaging systems, resulting in a bulky system that is easily disturbed by the environment. Metasurfaces are optical elements with characteristic dimensions in the nanometer or micrometer scale and has strong light field regulation capability. The integration of metasurfaces in microscopic systems can achieve directionally independent single shot quantitative phase imaging, along with the advantages of having a small, lightweight, and easily integrated structure. This study reviews the principles of classic phase imaging techiques, and provides a detailed introduction to the principles of techniques based on three types of metasurfaces: shear interference, phase contrast, and transport of intensity equation. The advantages, disadvantages, and applicable scenarios of the different techniques are compared, and then the challenges faced by metasurfaces in the field of phase imaging are pointed out. Finally, future development trends are prospected.