This paper reviews our work simulating human thinking with the LISA model. Human mental representations are both flexible and structure-sensitive—properties that jointly present challenging design requirements for a model of the cognitive architecture. LISA satisfies these requirements by representing relational roles and their fillers as patterns of activation distributed over a collection of semantic units (achieving flexibility) and binding these representations dynamically into propositional structures using synchrony of firing (achieving structure-sensitivity). The resulting representations serve as a natural basis for memory retrieval, analogical mapping, analogical inference and schema induction. In addition, the LISA architecture provides an integrated account of effortless “reflexive” forms of inference and more effortful “reflective” inference, serves as a natural basis for integrating generalized procedures for relational reasoning with modules for more specialized forms of reasoning (e.g., reasoning about objects in spatial arrays), provides an a priori account of the limitations of human working memory, and may serve as a platform for understanding the neural basis of symbolic thought.