Is the framework of Universal Dependencies (UD) compatible with findings from linguistic typology? To address this question, we need to systematically review how UD represents linguistic constructions in the world's languages, and how it handles the range of morphosyntactic variation attested in linguistic typology. In this paper, we start this review by discussing reference and modification constructions. The review shows that, although UD can represent all major constructions in this area, there are a number of cases where UD categories do not align systematically with a typological classification of constructions, and where constructional similarity is therefore not transparent across languages. We also identify limitations in the representation of certain morphosyntactic strategies, notably indexation and linkers. To overcome these limitations, we propose a number of revisions that may be considered for future versions of UD.