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Since its invention, the calculus of variations has been a central field of mathematics and physics, providing tools and techniques to study problems in geometry, physics and partial differential equations. On the one hand, steady progress is made on long-standing questions concerning minimal surfaces, curvature flows and related objects. On the other hand, new questions emerge, driven by applications to diverse areas of mathematics and science. The July 2012 Oberwolfach workshop on the Calculus of Variations witnessed the solutions of famous conjectures and the emerging of exciting new lines of research.