Advances in the understanding of static large deflection, postbuckling, and nonlinear dynamic response by using the analytical method are summarized for laminated elastic plates. In the case of symmetric laminates, bending-stretching coupling vanishes. The classical nonlinear theory of orthotropic or anisotropic plates applies, and references are also presented for these plates. A nonlinear shear-deformable theory of generally laminated plates and a general method of solution are briefly reviewed for a wide class of boundary conditions. Several effects, which complicate the geometric nonlinear behavior of composite plates, discussed in this survey paper are: transverse shear and normal stresses, rotatory and in-plane inertia, initial in-plane edge forces, geometric imperfections, cutouts, and nonclassical boundary conditions.