This Element outlines current issues in the study of speech acts. It starts with a brief outline of four waves of speech act theory, that is, the philosophical, the experimental, the corpus-based and the discursive approaches. It looks at some of the early experimental and corpus-based methods and discusses their more recent developments as a background to the most important trends in current speech act research. Discursive approaches shift the focus from single utterances to interaction and interactional sequences. Multimodal approaches show that the notion of 'speech act' needs to be extended in order to cover the multimodality of communicative acts. And diachronic approaches focus on the historicity of speech acts. The final section discusses some open issues and potential further developments of speech act research.