As an important topic in the field of surface deformation, flattening and folding has become a research hotspot in recent years. In order to satisfy the constraints of aesthetics and mechanics, it is necessary to design flattening and folding structure. Using computer technology to simulate the flattening and folding of objects, geometric structures that meet the constraints can be designed. At present, flattening and folding are widely used in industrial design, biomedicine, intelligent robot, furniture design, and other fields. This paper mainly introduces the research status of computer flattening and folding objects in recent years. Firstly, the algorithms of flattening and folding are classified, and the basic ideas of each method are briefly described. Then, the various methods are analyzed, and their advantages and limitations are summarized. Finally, the corresponding evaluation criteria are given for further comparison. The flattening and folding method of curved surface has been developed and innovated step by step, and tends to be mature. However, due to the complex practical application requirements, the deformation results may not be perfect. A review of the current flattening and folding methods can provide research direction for future work.