We provide a conceptual framework for understanding similarities and differences among various schemes of compositional representation, emphasizing problems that arise in modelling aspects of human language. W e propose six abstract dimensions that suggest a space of possible compositional schemes. Temporality turns out to play a key role in defining several of these dimensions. From studying how schemes fall into this space, it is apparent that there is no single crucial difference between AI and connectionist approaches to representation. Large regions of the space of composition^ schemes remain unexplored, such as the entire class of active, dynamic models that do composition in time. These models offer the possibility of parsing real-time input into useful segments, and thus potentially into linguistic units like words and phrases.