Dynamics semantics was developed to account for non-truthconditional aspects of meaning in a compositional way. Major topics in the dynamic literature are anaphoricity, epistemic modalities, and presuppositions. This dissertation aims at extending the coverage of this approach to Topic-Comment structuring. After reviewing some well-established semantic theories, it is shown that none of it is able to explain certain properties of definite and indefinite expressions. It is argued that a satisfactory analysis requires a) a dynamic setup, and b) a notion of context that is more complex than it is commonly assumed. The author presents a formal semantic theory that fulfills these requirements. It is used to explain certain apparently heterogenous phenomena like bridging, the strong/weak ambiguity of cardinal expressions, and the proportion problem.