Much of the work on diagrammatic reasoning assumes that the structure of the diagrams has already been determined. This is not the case when dealing with diagrams in the published scientific literature. So we are building a system that can understand these diagrams, starting from the graphics primitives such as lines and polygons and resulting in symbolic and veridical representations of the diagram structure. To date we have pursued an approach based on Graphics Constraint Grammars which describe diagram components as a hierarchically structured collection satisfying various geometric constraints. The grammars encode the conventional aspects of diagram structure as well as the informational aspects related to perceptual grouping. As part of this, we have developed spatially indexed data structures that allow the direct spatial storage and recovery of diagrammatic and symbolic information.