Jeroen Groenendijk \& Martin Stokhof \& Frank Veltman, {\em Coreference and Contextually Restricted Quantification}, to appear in: Proceedings SALT V, DMLL Publications, Cornell. The aim of this paper is to argue that update semantics is a natural framework for contextually restricted quantification, and to illustrate its use in the analysis of anaphoric definite descriptions and certain other anaphoric terms. The discussion in the paper remains informal, but takes place against the background of the system of update semantics for the language of modal predicate logic presented in {\em Coreference and Modality}.