Despite our increasing reliance on diagrams as a form of communication there is little guidance for educators on how to teach students to think critically about diagrams in general. Consequently, while we teach students to read specific kinds of diagrams within specific contexts, we lack a coherent approach to thinking critically about diagrams per se. This paper presents a theoretical framework for a general diagrammatic literacy, based on conceptualising diagrams in terms of function rather than form. Approaching diagrams functionally generates a framework for thinking critically about diagrams (in general) that is simple, robust and exhaustive. In addition to this functional approach, the role of context and language to the internal definition of any given diagram is emphasised. [Author abstract]