Grammar-based natural language processing has reached a level where it can `understand' language to a limited degree in restricted domains. For example, it is possible to parse textual material very accurately and assign semantic relations to parts of sentences. An alternative approach originates from the work of Shannon over half a century ago [41], [42]. This approach assigns probabilities to linguistic events, where mathematical models are used to represent statistical knowledge. Once models are built, we decide which event is more likely than the others according to their probabilities. Although statistical methods currently use a very impoverished representation of speech and language (typically finite state), it is possible to train the underlying models from large amounts of data. Importantly, such statistical approaches often produce useful results. Statistical approaches seem especially well-suited to spoken language which is often spontaneous or conversational and not readily amenable to standard grammar-based approaches.