Jeroen Groenendijk \& Martin Stokhof \& Frank Veltman, {\em Coreference and Modality}, to appear in: S.~Lappin~(ed.), Handbook of Contemporary Semantic Theory, Blackwell, Oxford. The paper presents an introduction to dynamic semantics. It does so by providing an update semantics for a language of modal predicate logic, enriched with deictic demonstratives. This system combines the dynamic semantics of predicate logic developed earlier by Jeroen Groenendijk and Martin Stokhof, with Frank Veltman's update semantics for a propositional language with modal operators. This combination is not a straightforward fusion of two distinct systems, but poses its own problems. The solution proposed in the paper involves a slight adaption of the notion of dynamic existential quantification, and makes use of a notion of referent system, as it was originally developed by Kees Vermeulen. The descriptive area is that of the interaction between indefinites, pronouns, and epistemic modalities, a subject renowned for the many puzzles it creates. The aim of the paper is to show that the dynamic perspective suggests interesting solutions to some of them.