In linguistics, pragmatics refers to meaning that is intended but not spelled out literally, i.e. it concerns what we humans understand beyond the semantic meaning of a sentence or text. Prominent examples of these include for instance scalar implicatures, such as the utterance “Some students failed", which is in its literal meaning compatible with a situation where all students failed, but which is usually interpreted as “some but not all" students having failed. Traditionally, these phenomena are modelled using game-theoretic models of human interaction (such as the rational speech act (RSA) model, Frank and Goodman, 2012). In my talk, I will provide an overview of how well recent large language models like ChatGPT are performing on pragmatic tasks - largely showing that they fail in many respects, and will then proceed to analyse what may be lacking from current LLMs.