Stamping forming is a method of pressure processing that has been widely applied to automotive manufacturing, household electrical appliance production, aviation, and other fields. Stamping friction plays a substantial role in the quality of stamping forming and the service life of the die. However, the problem of friction in stamping forming has not yet been solved due to several critical difficulties. In particular, with the application of hot forming technology and new lightweight materials in stamping forming, such as advanced high-strength steel sheets, aluminum alloy sheets, and carbon fiber materials, stamping friction has become more complex. Therefore, it is of paramount practical significance to study stamping friction. In this paper, state of the art research concerning the mechanism and factors influencing friction in stamping forming is reviewed. Investigations of the friction mechanism are described, starting by introducing the development process of traditional and modern friction theory. The present friction mechanism fails to adequately describe the frictional process occurring in stamping forming due to complex and variable factors. A survey of existing works reveals several gaps in the study of factors that influence stamping forming: the friction model is very fragile; the accuracy is not high because only a few factors are considered; and more importantly, some important factors are often ignored, such as temperature and coating. Therefore, different dynamic friction models with multifactor coupling should be established for different stamping processes and materials to fully reflect the characteristics and mechanisms of stamping friction. The present review is aimed at providing an insight into the shortcomings of the existing research background, and it demonstrates the enormous potential for further investigation and innovation in the field of friction of stamping forming.