The book presents mathematical and mechanical aspects of the theory of plates and shells, applications in civil, aero-space and mechanical engineering, as well in other areas. The focus relates to the following problems:- comprehensive review of the most popular theories of plates and shells,- relations between three-dimensional theories and two-dimensional ones,- presentation of recently developed new refined plates and shells theories (for example, the micropolar theory or gradient-type theories),- modeling of coupled effects in shells and plates related to electromagnetic and temperature fields, phase transitions, diffusion, etc.,- applications in modeling of non-classical objects like, for example, nanostructures,- presentation of actual numerical tools based on the finite element approach.