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Abnormal refraction and reflection refers to the phenomenon in which light does not follow its traditional laws of propagation and instead is subject to refraction and reflection at abnormal angles that satisfy a generalization of Snell’s law. Metasurfaces can realize this phenomenon through appropriate selection of materials and structural design, and they have a wide range of potential applications in the military, communications, scientific, and biomedical fields. This paper summarizes the current state of research on abnormal refractive and reflective metasurfaces and their application scenarios. It discusses types of abnormal refractive and reflective metasurfaces based on their tuning modes (active and passive), their applications in different wavelength bands, and their future development. The technical obstacles that arise with existing metasurface technology are summarized, and prospects for future development and applications of abnormal refractive and reflective metasurfaces are discussed.