As the basis of metal forming theory, material constitutive model plays an important role in machining simulation. In this paper, the research status of constitutive relation in metal cutting is reviewed. It mainly introduces the advantages and disadvantages of several typical constitutive models, their applications in the actual machining process and their correction, also the acquisition and correction methods of original parameters of the constitutive model. Finally, some deficiencies in the constitutive model of metal cutting and the future research direction are analyzed.