Abstract: Edge detection has been widely applied in autonomous driving, pattern recognition, biomedical imaging, and other fields. Among various approaches, optical edge detection has garnered significant attention from researchers due to its advantages of high speed and parallel processing capabilities. As an emerging optical field modulation device, metasurfaces enable precise manipulation of light fields within extremely compact spatial dimensions, and have been extensively employed in optical edge detection systems. Design methodologies for metasurface-based optical edge detection can be classified into two major categories: the spatial Fourier transform method and the Green's function method. The spatial Fourier transform method utilizes metasurfaces as filtering elements in 4F (f represents the focal length) systems to achieve precise modulation of the optical field spectrum. The Green's function method employs a single metasurface to directly modulate incident light at different angles, thereby realizing specific optical transfer functions. This review summarizes the principles and characteristics of these two methodologies, presents an overview of related research progress both domestically and internationally, identifies current challenges, and proposes potential directions for future development.