In this contribution, a refined two-dimensional theory, based on higher-order kinematic models and the equivalent single-layer approach, is presented for the static and dynamic analysis of laminated doubly curved shell structures made of advanced materials and subjected to arbitrary loading and boundary conditions. Each layer of the structure is made of advanced materials, including short- and long-fiber-reinforced composites, lattice and honeycomb cores, and functionally graded materials, among others. Furthermore, the effect of the reinforcement with agglomerated carbon nanotubes (CNTs) is studied, with the material properties homogenized through an analytical procedure based on the Mori–Tanaka approach. The fundamental equations are derived in curvilinear principal coordinates from the Hamilton principle, expressed in both strong and weak forms. A numerical solution is obtained using the Generalized Differential and Integral Quadrature methods. In the post-processing step, an efficient recovery procedure reconstructs the three-dimensional (3D) response of the structure by means of the equilibrium equations. In addition, mode frequencies and shapes are successfully evaluated for dynamic analysis. The model is systematically validated against 3D solutions from finite-element-based commercial software for both mode frequencies and stress distribution. Then, parametric investigations are conducted through various numerical examples, pointing out the sensitivity of the model to geometric and material parameters, including agglomeration parameters, volume fractions of constituent materials, kinematic models, and curvature effects, among others. The proposed approach is demonstrated to be more computationally efficient than classical numerical methods and allows a straightforward modification of the governing parameters in each simulation. The results of the analysis offer a useful tool for studying the static and dynamic behavior of these structures, thus allowing us to adopt advanced structural components in the design process. In this way, new possibilities can arise for a broader application of these structures and materials.