All of us engage in and make use of valid reasoning, but the reasoning we actually perform differs in various ways from the inferences studied by most (formal) logicians. Reasoning as performed by human beings typically involves information obtained through more than one medium. Formal logic, by contrast, has thus far been primarily concerned with valid reasoning which is based on information in one form only, i.e. in the form of sentences. Recently, many philosophers, psychologists, logicians, mathematicians, and computer scientists have become increasingly aware of the importance of multi-modal reasoning and, moreover, much research has been undertaken in the area of non-symbolic, especially diagrammatic, representation systems. This entry outlines the overall directions of this new research area and focuses on the logical status of diagrams in proofs, their representational function and adequacy, different kinds of diagrammatic systems, and the role of diagrams in human cognition.