Abstract: Composite sandwich structures are widely used in aerospace, shipbuilding and other fields due to their excellent strength- and stiffness-to-weight ratio and small apparent density. From the three aspects of theoretical research, simulation analysis and experimental research, this paper summarizes the current situation of quasi-static stability research of honeycomb, foam, lattice and foldcore sandwich structures. The research on honeycomb sandwich structure is relatively mature, and further research should focus on the application field. The foam sandwich structure needs to be strengthened in the panel/core interface, and the fiber stitching technology can be considered. The theory of foldcore sandwich structure needs further study and has great potential. The lattice sandwich structure has stronger anti-buckling ability than other structures, but there is still a problem of face/core bonding. The problem of the quasi-static stability of the composite sandwich structure is mainly focused on the bonding of the face/core. The fiber stitching technology can effectively enhance the performance of the face/core. The research in this area has a strong potential for enhancing the stability of the composite sandwich structure.