Within Artificial Intelligence, diagrammatic reasoning is becoming an increasingly important area of research. This talk describes how we have used two cognitively-based reasoning techniques -- *qualitative spatial reasoning* and *analogical encoding* -- to build better, more flexible diagrammatic reasoners. First, we describe GeoRep, a qualitative spatial reasoner that builds spatial descriptions from vector-based line drawings. GeoRep's flexibility as a spatial reasoner is based on a two-level architecture, where cognitively-plausible low-level visual relations are used support a broad range of domain-specific diagrammatic representations. GeoRep has been used successfully in several diagrammatic domains, including studies of abstract figure perception, military course-of-action diagrams, and geographic reasoning. We next describe MAGI, our model of repetition and symmetry detection (which is based on existing structure-mapping models of analogy and similarity). Repetition and symmetry are often used in diagrams to provide contrasts and establish opposing concepts. Using a technique called analogical encoding, we show how MAGI allows us to model the cognitive processes humans use when reading repetition-based diagrams by aligning visual and conceptual structure.