Computational linguistics builds models that can usefully process and produce language and that can increase our understanding of linguistic phenomena. From the computational perspective, language data are particularly challenging notably due to their variable degree of idiosyncrasy (unexpected properties shared by few peer objects), and the pervasiveness of non-compositional phenomena such as multiword expressions (whose meaning cannot be straightforwardly deduced from the meanings of their components, e.g. red tape, by and large, to pay a visit and to pull one’s leg) and constructions (conventional associations of forms and meanings). Additionally, if models and methods are to be consistent and valid across languages, they have to face specificities inherent either to particular languages, or to various linguistic traditions. These challenges were addressed by the Dagstuhl Seminar 21351 entitled "Universals of Linguistic Idiosyncrasy in Multilingual Computational Linguistics", which took place on 30-31 August 2021. Its main goal was to create synergies between three distinct though partly overlapping communities: experts in typology, in cross-lingual morphosyntactic annotation and in multiword expressions. This report documents the program and the outcomes of the seminar. We present the executive summary of the event, reports from the 3 Working Groups and abstracts of individual talks and open problems presented by the participants.