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Since its invention by Newton, the calculus of variations has formed one of the central techniques for studying problems in geometry, physics, and partial differential equations. This trend continues even today. On the one hand, slow but steady progress is made on long-standing questions concerning minimal surfaces, curvature flows, and related geometric objects. Basic questions also remain in such areas as mathematical physics and general relativity. On the other hand, new types of question emerge, driven by applications from economics and engineering to materials science, whose solution will depend on developing ideas and techniques in this classical branch of analysis. The July 2010 Oberwolfach workshop on the Calculus of Variations showcased a blend of continued progress in traditional areas with surprising developments which emerged from the exploration of new lines of research.