In the study of the meaning of natural language expressions, the sentence level provides a natural entry point. Its relevance depends, of course, on the focus we want to put on meaning: as related to thoughtThought, to communication, to truth, etc. In this paper, we concentrate on the model theoretic view of meaning, in particular via first-order logic representation. More specifically, we present phenomena that illustrate the challenges posed by discourse to truth-conditional semanticsSemantics and compositionalityCompositionality. We show that proposals to address these challenges rely on the additional device of contexts Context and on the way sentences can access and modify these contextsContext. This capability is usually referred to as the context change potential Context change potential of a sentence. Depending on the phenomenon, contextsContext need to represent different kinds of informationInformation: propositions, discourse referents, and variations on these elements. We also show that taking into account the rhetorical structureStructure!rhetorical structure, discourse structure of discourse leads to even richer structuring of the contextContext. Parallel to the presentation of the phenomena, we concentrate on formalismsFormalism giving an account of the dynamicsDynamics of discourse. We introduce the well-established formalismsFormalism of Discourse Representation Theory (DRT)DRT (Discourse Representation Theory), Dynamic Predicate Logic (DPLLogic!DPL (Dynamic Predicate Logic)), and the more recently developed approach based on continuationContinuation semanticsSemantics. Finally, we introduce Segmented Discourse Representation Theory (SDRTSDRT (Segmented Discourse Representation Theory)) which combines the effects of dynamicsDynamics and discourse structureStructure!rhetorical structure, discourse structure.