This book is a collection of survey articles in a broad field of the geometrical theory of the calculus of variations and its applications in analysis, geometry and physics. It is a commemorative volume to celebrate the sixty-fifth birthday of Professor Demeter Krupka, one of the founders of modern geometric variational theory, and a major contributor to this topic and its applications over the past thirty-five years. All the authors invited to contribute to this volume have established high reputations in their field. The book will exclusively provide a variety of important results, techniques and applications that are usually available only by consulting original papers in many different journals. It will be of interest to researchers in variational calculus, mathematical physics and the other related areas of differential equations, natural operators and geometric structures. Also, it will become an important source of current research for doctoral students and postdoctorals in these fields.