Polysemy, understood as instances of a single linguistic expression having multiple related senses, is not a homogenous phenomenon. There are regular (apparently, rule‐based) cases and irregular (resemblance‐based) cases, which have different processing profiles. Although a primary source of polysemy is pragmatic inference, at least some cases become conventionalised and linguistically encoded. Three main issues are discussed: (a) the key differences between regular and irregular cases and the role, if any, of a “core meaning”; (b) the distinction between pragmatic polysemy and (...) semantic polysemy; and (c) the role of syntactic meaning in both generating and constraining polysemy. (shrink)