This book analyses the multifield behavior of doubly-curved shells made of anisotropic and advanced materials. These materials include fiber reinforced composite materials, carbon nanotubes, variable angle tow composites, honeycomb cells, anisogrid, and functionally graded materials. Considering the three different approaches to studying the mechanical and multifield behavior of anisotropic doubly-curved shell structures, the book comprehensively explains the mathematical steps necessary for each method based on curvilinear principal coordinates. Furthermore, an isogeometric mapping technique is illustrated to investigate arbitrarily-shaped structures. The modeling strategies presented in the book are three-dimensional elasticity theory, along with the Equivalent Single Layer (ESL) and the Layer-Wise (LW) approach. The book focuses on Higher-order Shear Deformation Theories (HSDTs) with unified formulation, and it also introduces classical theories like the Kirchoff–Love theory and the First-order Shear Deformation Theory (FSDT). It also illustrates strong and weak formulations of the governing equations of motion and provides numerical results for several structural components as examples. Relevant to studies in plates and shells, advanced materials, multifield analysis, vibration and stress, the book is the ideal companion for engineers and students in the area of structural, applied, and computational mechanics.