 Situation semantics was developed as an alternative to possible worlds semantics. In situation semantics, linguistic expressions are evaluated with respect to partial, rather than complete, worlds. There is no consensus about what situations are, just as there is no consensus about what possible worlds or events are. According to some, situations are structured entities consisting of relations and individuals standing in those relations. According to others, situations are particulars. In spite of unresolved foundational issues, the partiality provided by situation semantics has led to some genuinely new approaches to a variety of phenomena in natural language semantics. In the way of illustration, this article includes relatively detailed overviews of a few selected areas where situation semantics has been successful: implicit quantifier domain restrictions, donkey pronouns, and exhaustive interpretations. It moreover addresses the question of how Davidsonian event semantics can be embedded in a semantics based on situations. Other areas where a situation semantics perspective has led to progress include attitude ascriptions, questions, tense, aspect, nominalizations, implicit arguments, point of view, counterfactual conditionals, and discourse relations.