Quantity implicatures have been intensely debated since Grice's programmatic work more than 50 years ago. Grice assumed quantity implicatures could be derived entirely from general maxims of conversation not specific to language. His approach, however, was seen to be insufficient because of maxim selection, alternative choice, and embedded implicatures. This chapter contrasts Grice's approach with two alternative approaches. First, it discusses the neo‐Gricean approach, which inserts a bit of grammar in the form of lexical scales into Grice's approach. Then it turns to the grammatical approach, which assumes that there is a mechanism akin to implicature computation that applies entirely within language. The empirical evidence currently favors the grammatical approach, but the approach is still undergoing rapid development.