In recent engineering applications, the demand of structural components of very complex shapes made of advanced and innovative materials has increased. For this reason, novel modelling strategies are necessary that can accurately predict the structural response while minimizing the computational cost. To this end, two-dimensional theories have been developed for doubly-curved shells made of advanced innovative materials. The accuracy of these theories depends on the kinematic description of the unknown field variable along the thickness direction. Higher Order Shear Deformation Theories (HSDTs) yield predictions whose accuracy can be compared to that of three-dimensional models. In this contribution, HSDTs are adopted in generalized Equivalent Single Layer (ESL) and Layer-Wise (LW) formulations to compute the static and dynamic deflections of doubly-curved shells characterized by complex lamination schemes with a three-dimensional variation of both the material properties and the orientation angle under various load cases and boundary conditions. Furthermore, the influence of agglomerated Carbon Nanotubes (CNTs) within the layers of the structure is investigated. The fundamental equations are derived from the Hamiltonian principle, and a numerical solution is provided using the Generalized Differential Quadrature (GDQ) and the Generalized Integral Quadrature (GIQ) method. An extensive set of case studies is presented, where the static and dynamic responses of panels of different curvatures and lamination schemes, derived from the present model, are successfully compared to those obtained from three-dimensional simulations developed with the Finite Element Method (FEM). Furthermore, extensive parametric investigations are carried out aiming at studying the effects of external boundary conditions, geometry and material properties on the structural response of some panels made of different kinds of materials, each of them homogenized as a continuum. The present model is a valid tool for modelling curved and layered structures made of advanced materials, which are very common in recent applications devoted to sustainability.