Abstract Universal dependencies (UD) is a framework for morphosyntactic annotation of human language, which to date has been used to create treebanks for more than 100 languages. In this article, we outline the linguistic theory of the UD framework, which draws on a long tradition of typologically oriented grammatical theories. Grammatical relations between words are centrally used to explain how predicate–argument structures are encoded morphosyntactically in different languages while morphological features and part-of-speech classes give the properties of words. We argue that this theory is a good basis for crosslinguistically consistent annotation of typologically diverse languages in a way that supports computational natural language understanding as well as broader linguistic studies.