Abstract:Calcium fluoride (CaF2) crystal is a very important optical crystal. It is widely used in optical instruments because of its high transmittance and good long-term radiation stability. Especially with the development of lithography technology to shorter wavelength, CaF2 has become the preferred material for extreme UV lithography objective. CaF2 is a typical brittle material with low fracture toughness. CaF2 optical surface is usually made by polishing, therefore, the polishing technology and process are very important. This paper summarizes the main machining methods, processes and research results of CaF2 , and introduces the ultra precision cutting and consolidated abrasive grinding methods involved in its rough machining stage; Paying more attention to ultra precision polishing, this paper comprehensively summarizes the principle and progress of float polishing, chemical mechanical polishing, fixed abrasive polishing, magnetorheological polishing, vibration assisted fixed abrasive polishing and ion-beam polishing, and the related processing methods mentioned are compared; Finally, the future development direction of CaF2 polishing technology is prospected. It aims to provide valuable reference for further research in the field of CaF2 processing.