The prediction of the hook load during casing insertion is one of the key factors for success. Due to its special wellbore trajectory, the frictional resistance during casing insertion in horizontal wells is higher than that in conventional wells. Therefore, accurately predicting the frictional resistance of casing insertion plays an important guiding role in the design and construction of horizontal well cementing. At present, many friction prediction analysis models have been developed in the industry, and relevant theoretical research and case analysis have been carried out. The commonly used analysis methods include Soft-String Model, Stiff-String Model and finite element method. Subsequent scholars used various theoretical methods to consider the friction analysis model of casing under various stress conditions on the basis of the three methods, but there is currently no relevant research that summarizes and analyzes the advantages and disadvantages of existing model algorithms, making it impossible to conduct model optimization in specific applications. Therefore, according to different basic theories, this paper classifieds and analyzes the current casing friction models, and discusses the existing technical bottlenecks in casing friction research and prediction as well as the next development direction, in order to provide guidance and help for the in-depth integration development of casing friction analysis in the future.