Cutting is a complex process involving many mechanical phenomena such as elastic deformation，plastic deformation，fracture，shear，impact and thermal field etc． Slip-line field theory is an effective mechanical tool for analyzing orthogonal cutting process． So far，many classical slip-line field models of orthogonal cutting at low and medium speeds have been established by scholars at home and abroad． Those models provide theoretical support for optimizing the cutting process parameters and guiding the cutting process． But with the development of high-speed cutting and micro-cutting，the current models cannot fully explain many physical phenomena in the cutting process． Therefore，the slip-line field models of orthogonal cutting in the past 70 years were reviewed，and the preconditions and applications of the models were analyzed and compared． The characteristics and disadvantages of various models were summarized． The slip line field models including uniform slip line field，non-uniform slip line field，free contact slip line field，restricted contact slip line field，slip line field in the transition zone between chip and work piece，blunt and circular slip line field of cutter，edge wear ( negative chamfering) slip line field，etc． were summarized． The future development of orthogonal cutting slip line field model was discussed， and laid a foundation for establishing orthogonal cutting slip line field model under the high speed cutting and micro cutting conditions．