The application of composite materials tothe submarine structure has become a development trend and research focus in the future due to the excellent mechanical and acoustic properties. For cylindrical shells as the main structure form of submarine, the research on vibration and sound radiation of composite laminated cylindrical shells has been widely carried out. Under the premise of meeting the underwater bearing capacity, the composite pressure cylindrical shell tends to be medium thick shell or even thick shell. In this situation, the transverse shear deformation, compression deformation and section warpage deformation along the thickness direction of the shell should not be ignored, for these factors have a direct impact on the accuracy of the description of the transverse vibration displacement field and the prediction of the sound radiation field around the shell. The existing shell theories mainly are classical shell theory, first-order shear deformation theory, high-order shear deformation theory, layer-wise theory, zig-zag theory and three-dimensional elastic theory, and these theories are relatively well developed. However, most of the studies are still limited to the vibration of orthotropic thin shell structures, and rarely involve the sound radiation of anisotropic thick shell structures. Furthermore, there is a lack of systematic summary and research on the applicability of these shell theories to the vibration and sound radiation of composite cylindrical shells. In this paper, the complexity of solving the vibration and sound radiation problems of composite materials is firstly explained based on the stiffness characteristics. Then, from the perspective of transverse vibration displacement field, the development process, research status and respective characteristics of these shell theories are summarized. Finally, the application scope and suggestions of these theories are given, some problems to be further studied are put forward and it is expected to provide references for the design and analysis of vibration and sound radiation of composite laminated cylindrical structures. © 2023 Cailiao Daobaoshe/ Materials Review. All rights reserved.