Calcium fluoride (CaF

2

) 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

 CaF

2

has become the preferred material for extreme UV lithography objective. CaF

2

is a typical brittle material with low fracture toughness. CaF

2

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 CaF

2

and introduces the ultra precision c

utting 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 CaF

2

polishing technology is prospected. It aims to provide valuable reference for further research in the field of CaF

2

processing.