Based on the principles of interference and diffraction, holographic imaging has achieved the reconstruction of amplitude and phase information of objects and thus has been widely studied. Metasurface is a new material with a subwavelength unit structure, which can realize many physical properties that are not available in nature. Furthermore, it can flexibly adjust and control the phase and amplitude of electromagnetic waves and complete the complex wave front adjustment and control through metasurface materials. Moreover, metasurface enhances the performancs of traditional spatial light modulators in imaging resolution, imaging efficiency, and imaging field-of-view angle. Consequently, the emergence of metasurface materials provides a solution for studying holographic imaging in the terahertz band. Therefore, this study first introduces the basic optical principles of holographic imaging. It then reviews current research progress of algorithms used in metasurface holographic imaging in different electromagnetic wave bands, especially in the terahertz band, domestically and internationally. Furthermore, it introduces the basic principles of several common metasurface design algorithms and the impact of various algorithms on imaging results. Additionally, it provides a comparative analysis and summary of these algorithms, which provides a reference for selecting metasurface design algorithms for terahertz band holographic imaging.