It is noted that increased demand for high performance structures has driven new development of smart materials and structures. Due to the intrinsic coupling effect between mechanical, magnetic, and electric fields, piezoelectric ceramics have been widely used as actuation devices and, because of features such as capacity for adaptive shape processing and self-diagnosis, have been used in transducers for underwater and biomedical imaging, active damping, Robot manipulators, high precision devices, micro sensors/actuators, vibration and noise control and the like. This book is a research monograph dealing with these multifield structures using Green's function and boundary element methodology. It presents a systematic and comprehensive coverage of theoretical and numerical modelling of multifield materials. The main emphasis is placed on fundamental concepts of the Green's function, the development of different Green's functions and boundary element formulations for coupled thermo-magneto-electro-elastic problems with various geometrical defects such as holes, cracks, half-plane boundary, and inclusion. The methods are described and derived with an objective to make them more accessible to research scientists, professional engineers and postgraduate students. In addition sections containing numerical examples are added demonstrating applications of the Green's functions. Many of the numerical presented in the book are important in their own right and also as test problems for validating new formulations. The book will be of benefit to all postgraduate students, researchers, professional engineers, and academic scientists requiring an accessible introduction to this subject, andlittle mathematical knowledge beyond the usual calculus is needed. It is hoped that the book can serve as a stimulant to encourage further development of theoretical and numerical approaches of coupled thermo-electro-elastic problems and to draw more attention in this field from researchers, engineers and scientists.