This contribution to Palgrave's "Advances" series addresses a wide range of issues that have arisen in post-Gricean pragmatic theory and presents a range of theoretical positions and approaches. Distinguished authors whose work is well known as lying at the interface of language, logic, linguistics, psychology and cognitive science contribute to the current lively debate within the field, with consideration of relevance theory, neo-Gricean pragmatics, optimality -theoretic pragmatics and experimental work. Among the specific topics covered are scalar implicature, lexical semantics and pragmatics, concepts and concept-adjustment, indexicality, speech acts, procedural meaning and the notion of 'constraint', the explicature-implicature distinction, numerical expressions, the semantics and pragmatics of negation and negative polarity items, and whether successful communication involves 'shared content'.