Most of modern formal semantics builds on a simple conception of meaning, imported from mathematical logic: the meaning of a sentence lies in its truth conditions. While this notion of sentence meaning has proved extremely fruitful, it is also limited; in particular, while it is suitable for statements, it is not naturally applicable to questions. Recent work on Inquisitive Semantics has produced a new formal notion of meaning which allows for a unified analysis of statements and questions. This new notion of meaning gives rise to a new and more general view on the relation logical consequence and on the semantics of connectives, quantifiers, and modalities. In the talk I will provide an introduction to inquisitive semantics and a brief overview of some of its applications to the analysis of natural language semantics.