The success of the WIMP interface, the convergence towards multimedia platforms and the growing use of the Internet combine to place new demands on the systems we use to communicate with one another. Proposals for iconic languages are not new but the computer offers the ability to incorporate interactivity and animation into iconic writing and reading systems. One approach to developing computer-based iconic communication systems derives from the visual arts (i.e. graphic design, illustration, film animation, documentary video, etc.). An alternative approach is derived from computational linguistics in that the syntactic or semantic structure of language is retained while iconic images are used in place of words. Differences between the study of natural language and the design of an iconic language are discussed and the components of one particular system, IconText, are described. Of particular interest is the attempt to capture some pragmatic aspects of communication, both in terms of conveying the intentions of the author and concerning the sequential delivery of the message.