Although diagrammatic representations have been a feature of human communication from early history, recent advances in printing and electronic media technologyhaveintroducedincreasinglysophisticatedvisualrepresentationsinto everyday life. We need to improve our understanding of the role of diagrams and sketches in communication, cognition, creative thought, and problem-solving. These concerns have triggered a surge of interest in the study of diagrammatic notations, especially in academic disciplines dealing with cognition, computation, and communication. We believe that the study of diagrammatic communication is best pursued as an interdisciplinary endeavor. The Diagrams conference series was launched to support an international research community with this common goal. After successful meetings in Edinburgh (2000) and Georgia (2002), Diagrams 2004 was the third event in the series. The Diagrams series attracts a large number of researchers from virtually all academic fields who are studying the nature of diagrammatic representations,their use in human communication, and cognitive or computationalmechanismsforprocessingdiagrams.Bycombiningseveralearlier workshop and symposium series that were held in the US and Europe – Reasoning with Diagrammatic Representations (DR), US; Thinking with Diagrams (TWD), Europe; and Theory of Visual Languages (TVL), Europe – Diagrams has emerged as a major international conference on this topic.