 H. P. Grice developed an influential theory to explain and predict conversational implicatures, and describe how they arise and are understood. The Cooperative Principle and associated maxims play a central role. Neo-Gricean theories modify Grice’s principles to some extent, and Relevance theories replace them with a principle of communicative efficiency. Problems for such principle-based theories include overgeneration, lack of determinacy, clashes, and the fact that speakers often have other goals. An alternative approach emphasizes that implicatures can be explained and predicted in all the ways intentions and conventions can be.