Dielectric metasurfaces-based planar optical spatial differentiator and edge detection have recently been proposed to play an important role in the parallel and fast image processing technology. With the development of dielectric metasurfaces of different geometries and resonance mechanisms, diverse on-chip spatial differentiators have been proposed by tailoring the dispersion characteristics of subwavelength structures. This review focuses on the basic principles and characteristic parameters of dielectric metasurfaces as first- and second-order spatial differentiators realized via the Green’s function approach. The spatial bandwidth and polarization dependence are emphasized as key properties by comparing the optical transfer functions of metasurfaces for different incident wavevectors and polarizations. To present the operational capabilities of a two-dimensional spatial differentiator in image information acquisition, edge detection is described to illustrate the practicability of the device. As an application example, experimental demonstrations of edge detection for different biological cells and a flower mold are discussed, in which a spatial differentiator and objective lens or camera are integrated in three optical pathway configurations. The realization of spatial differentiators and edge detection with dielectric metasurfaces provides new opportunities for ultrafast information identification in biological imaging and machine vision.