The principle of compositionality of meaning is the foundation of semantic theory. With function application as the main rule of combination, compositionality requires complex expressions to be interpreted in terms of function-argument structure. Type theory lends itself to an insightful representation of many combinations of a functor and its argument. But not all well-formed linguistic combinations are accounted for within classical type theory as adopted by Montague Grammar. Conflicts between the requirements of a functor and the properties of its arguments are described as type mismatches. Three solutions to type mismatches have been proposed within enriched type theories, namely type raising, type shifting, and type coercion. This article focusses on instances of type coercion. We provide examples, propose lexical and contextual restrictions on type coercion, and discuss the status of coercion as a semantic enrichment operation. The paper includes a special application of the notion of coercion in the domain of tense and aspect. Aspectual coercion affects the relationship between predicative and grammatical aspect. We treat examples from English and Romance languages in a cross-linguistic perspective.