Geometric data is now ubiquitous. Such 3D content is either acquired using LiDAR scans, MRI scans, etc., or created using 3D modelers, or obtained as output of simulation processes. The data, however, come in low-level representations (e.g., points, polygons, voxel grids) and begets little understanding of the underlying objects or processes. This is unfortunate since such data have significant redundancies as they often measure related entities (e.g., humans in different poses, same room across multiple configurations, or chairs having different styles). While the data can potentially reveal significant self-similarities among objects and correlations across related objects, we are missing critically-needed tools for such analysis.Hence, I propose to develop mathematical frameworks and computational tools to extract, represent, manipulate, and utilize relations among 3D model collections. Essentially, I propose to factorize model collections into consistent structures (i.e., relations among parts in and across multiple objects) and low-dimensional variations, with local geometric details playing a subordinate role. Jointly analyzing model collections can further reveal relationshipsbetween form and their functions (e.g., chairs typically will have consistent back-seat relations, even if at the level of vertices the underlying models can be very different). This requires solving two coupled problems:(i) jointly analyzing large model collections to decouple consistent structure from dominant modes of variations, and (ii) using the information towards next generation form-finding possibilities.The grand goal is to lay the foundations of structure-aware geometry processing where computationally extracted geometric relations and constraints are automatically conformed to with potentially far-reaching implications in a range of disciplines like science, engineering, medicine, and product design.