This paper presents the state of art in the field of composite shells with focus on stress analysis, buckling and post-buckling responses under mechanical and thermal loading. Many researchers have investigated the buckling and post-buckling responses of cylindrical, conical, spherical, thin and thick composite shells with single and doubly curved shells under mechanical and thermal loading. From the literature it can be inferred that hydrostatic pressure, axial compression and thermal environment influence the buckling behavior of laminated composite shell significantly. An effort is taken to review the research on buckling and post-buckling responses of cylindrical and conical shaped shells under mechanical and thermal loading and their behavior during buckling and post-buckling conditions. POLYM. COMPOS., 39:4231–4242, 2018. © 2017 Society of Plastics Engineers. © 2017 Society of Plastics Engineers