Digital models of physical shapes are becoming ubiquitous in our economy and life. Such models are sometimes designed ab initio using CAD tools, but more and more often they are based on existing real objects whose shape is acquired using various 3D scanning technologies. In most instances, the original scanner data is just a set, but a very large set, of points sampled from the surface of the object. We are interested in tools for understanding the local and global structure of such large-scale scanned geometry for a variety of tasks, including model completion, reverse engineering, shape comparison and retrieval, shape editing, inclusion in virtual worlds and simulations, etc. This talk will present a number of point-based techniques for discovering global structure in 3D data sets, including partial and approximate symmetries, shared parts, repeated patterns, etc. It is also of interest to perform such structure discovery across multiple data sets distributed in a network, without actually ever bring them all to the same host.