The retrieval of phase information from the complex amplitude of light waves is a pivotal area of research in various scientific and engineering fields, as phase carries essential information about the propagation of light, profoundly influencing the advancement of imaging and intelligent sensing technologies. Phase recovery wavefront reconstruction techniques, leveraging advanced optimization algorithms and specialized imaging setup, extract the challenging-to-detect phase information from intensity data gathered by imaging sensors. Phase recovery wavefront reconstruction technique is one of the key methods enabling the exploration of both micro and macro worlds, extensively applied in diverse fields such as biological microscopy, industrial inspection, and astronomical observation. This paper begins by outlining both interferometric and non-interferometric wavefront reconstruction techniques and their respective applications. Subsequently, it reviews the fundamental principles and developmental trajectory of phase retrieval algorithms in wavefront reconstruction. This encompasses a preliminary exploration of prevalent phase retrieval methodologies, including alternating projection phase retrieval algorithms, ptychography imaging, and phase retrieval wavefront reconstruction techniques integrating modulation constraints and deep learning. The article concludes by summarizing the entire discourse and outlining prospective directions for the future development of phase retrieval wavefront reconstruction technology, which include the enhancement of algorithms and the development of imaging systems and devices.