Analytical and numerical models have been implemented in this work to study multifield problems for multilayered structures. The dissertation is organized in three main parts: an extension of the geometrical relations and constitutive equations to multifield problems and multilayered plates and shells; the introduction of Carrera's Unified Formulation (CUF), the use of variational statements, and their extension to multifield problems; the results of several multifield couplings. Constitutive equations for multifield problems are given in the first part and they are extended to functionally graded materials by employing opportune thickness functions to describe the physical properties that continuously change in the thickness direction. The multifield constitutive equations, obtained in a generalized way by employing thermodynamic considerations, are discussed for several multifield couplings and rewritten opportunely for the case of mixed models. Geometrical relations for plates and shells are discussed, with particular attention to their extension to multifield problems. The second part is devoted to CUF, with the introduction of a general and unified manner of describing the variables related to mechanical, thermal and electrical fields in multilayered plates and shells. The proposed two-dimensional models are defined as refined or advanced, according to the considered variational statement: refined models are based on the principle of virtual displacements (PVD), advanced models employ Reissner's mixed variational theorem (RMVT). The third part is about the results of the pure mechanical analysis, the thermo-mechanical analysis and the electro-mechanical coupling.