Compositional Intelligence (CI) is the study of AI models, and models of intelligence more broadly, based on an explicit meaningful compositional structure. Such models are built from ‘building blocks’ of elementary components and processes which are combined and re-composed, as formalized mathematically through category theory and the graphical language of string diagrams. Compositional models may be implemented computationally either using quantum computers, or classically, such as via neural networks. Examples of meaningful compositional structure include linguistic, causal, logical, or conceptual structure. Benefits of such structure include reasoning and inference capabilities, a strong kind of intrinsic interpretability, training efficiency, generalization, and efficient rewrite systems for simplification.