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Due to recent developments in modeling software and advances in acquisition techniques for 3D geometry, large numbers of shapes have been digitized. Existing datasets include millions of real-world objects, cultural heritage artifacts, scientific and engineering models, all of which capture the world around us at nano- to planetary scales. As large repositories of 3D shape collections continue to grow, understanding the data, especially encoding the inter-model similarity and their variations, is of the utmost importance. In this dissertation we address the challenge of deriving structure from a large, unorga-nized, and diverse collection of 3D polygonal models. By structure we refer to how objects correspond to each other, how they are segmented into semantic parts, and how the parts deform and change across the models. While previous work has generally dealt with small and relatively homogeneous datasets, in this dissertation we concentrate on diverse and large collections. Our contribution is three-fold. First, we present an algorithm for establishing correspon-dences between pairs of shapes related by a non-uniform deformation. Second, we develo