This paper gives an outline of a research project conceming Danish support verb constructions (German: Funktionsverbgefiige), a phenomenon previously confined to the periphery of Danish linguistics. The following issues are addressed: problems in defining support verb constructions, the inventory of a list of Danish support verbs, their treatment in monolingual and bilingual dictionaries, and an ongoing study of three Danish support verbs (foretage 'undertake/make/do', lave 'make/do', gøre 'do/make'). The paper suggests a grading of support verb constructions according to scope for modification (unrestrictedness/idiomaticity) and it advocates a semantic approach. A semantic classification of verbs can constitute the basis for predicting which verbal nouns, i.e. the substantival counterparts of verbs, may combine with the different support verbs.