Abstract: Laminated composite plates and shells are made from a variety of materials. They have quite different mechanical features compared with those made of single material, such as uncertain principal direction of the material, discontinuity of material between layers, highly geometrical and material nonlinearity, etc. Their failure modes include matrix cracking, debonding, delamination, crack deflection, multi delamination and delamination propagation, which are much more complex than those of single material. Based on different considerations, various methods have been proposed by scholars from different countries to study the failure of laminated composite plates and shells. This paper summarizes the fundamental theory of linear mechanics and reviews the development of nonlinear theories for laminated plates and shells. In particularly, theoretical systems and basic formulas are expatiated for the classical nonlinear theory of large deformation, the first order shear deformation theory, the high order shear deformation theory, the zig-zag theory, and the layer-wise theory. The relevance and differences among these theories are stated. Current research progress in the field of nonlinear mechanics for laminated composite plates and shells are overviewed and the latest achievements are introduced in research hotspots regarding the failure mechanism and optimization design of typical laminated composite plates and shells, the failure mechanism of laminated composite plates and shells in complex environments, material nonlinearity of composite plates and shells, failure mechanism of fiber reinforced delaminated composite plates and shells, and so on. Based on the review, prospects for future research in the area of nonlinear mechanics of laminated composite plates and shells are proposed.