It is well-documented that Multiword Expressions (MWEs) pose a unique challenge to a variety of NLP tasks such as machine translation, parsing, information retrieval, and more. For low-resource languages such as Irish, these challenges can be exacerbated by the scarcity of data, and a lack of research in this topic. In order to improve handling of MWEs in various NLP tasks for Irish, this thesis will address both the lack of resources specifically targeting MWEs in Irish, and examine how these resources can be applied to said NLP tasks. We report on the creation and analysis of a number of lexical resources as part of this PhD research. Ilfhocail, a lexicon of Irish MWEs, is created through extract- ing MWEs from other lexical resources such as dictionaries. A corpus annotated with verbal MWEs in Irish is created for the inclusion of Irish in the PARSEME Shared Task 1.2. Additionally, MWEs were tagged in a bilingual EN-GA corpus for inclusion in experiments in machine translation. For the purposes of annotation, a categorisation scheme for nine categories of MWEs in Irish is created, based on combining linguistic analysis on these types of constructions and cross-lingual frameworks for defining MWEs. A case study in applying MWEs to NLP tasks is undertaken, with the exploration of incorporating MWE information while training Neural Machine Translation systems. Finally, the topic of automatic identification of Irish MWEs is explored, documenting the training of a system capable of automatically identifying Irish MWEs from a variety of categories, and the challenges associated with developing such a system. This research contributes towards a greater understanding of Irish MWEs and their applications in NLP, and provides a foundation for future work in exploring other methods for the automatic discovery and identification of Irish MWEs, and further developing the MWE resources described above.