This practical Advanced Course aims to introduce students with computational linguistics backgrounds to incremental language processing for Spoken Dialogue Systems (SDS). Students will be shown the benefits of incrementality for improving speed, naturalness and fluidity of conversing with machines. Concretely, we will be looking at SDSs where processing information from user speech on a word-by-word basis is crucial. The course will cover how to deal with various natural, incremental phenomena in dialogue – such as spoken disfluencies, utterance continuations and interruptions – which standard dialogue systems cannot deal with, using incremental, semantically driven natural language understanding and generation models. Each session is divided into a lecture, and a practical. During the practicals students work gradually towards building their own fully incremental SDS in a small domain, using the technical tools and API that we will provide. Our aim is that by the end of the course, students will appreciate the multi-faceted complexity of real-time language processing in dialogue.