This article provides an account of the distribution and interpretation of polarity particles in responses, starting with yes and no in English, and then extending the coverage to their crosslinguistic kin. Polarity particles are used in responses to both declarative and interrogative sentences, and thus provide a window onto the semantics and discourse effects of such sentences. We argue that understanding the distribution and interpretation of polarity particles requires a characterization of declaratives and interrogatives that captures a series of challenging similarities and differences across these two sentence types. To meet this challenge we combine and extend insights from inquisitive semantics, dynamic semantics, and commitment-based models of discourse. We then provide a full account of the English data that leads to a typology of polarity particles and a series of crosslinguistic predictions. These predictions are checked against data from Romanian, Hungarian, French, and German, languages that contrast with English in that they have ternary polarity particle systems, and contrast with one another in further subtle ways.