Despite enjoying the status of an official EU language, Irish is considered a minority language. As with most minority languages, it is a `low-density' language, which means it lacks important linguistic and Natural Language Processing (NLP) resources. Relative to better-resourced languages such as English or French, for example, little research has been carried out on computational analysis or processing of Irish. Parsing is the method of analysing the linguistic structure of text, and it is an invaluable processing step that is required for many different types of language technology applications. As a verb-initial language, Irish has several features that are uncharacteristic of many languages previously studied in parsing research. Our work broadens the application of NLP methods to less studied language structures and provides a basis on which future work in Irish NLP is possible. We report on the development of a dependency treebank that serves as training data for the first full Irish dependency parser. We discuss the linguistic structures of Irish, and the motivation behind the design of our annotation scheme. Our work also examines various methods of employing semi-automated approaches to treebank development. We overcome the relatively small pool of linguistic and technological resources available for the Irish language with these approaches, and show that even in early stages of development, parsing results for Irish are promising. What counts as a sufficient number of trees for training a parser varies according to languages. Through empirical methods, we explore the impact our treebank's size and content has on parsing accuracy for Irish. We also discuss our work in crosslingual studies through converting our treebank to a universal annotation scheme. Finally we extend our Irish NLP work to the unstructured user-generated text of Irish tweets. We report on the creation of a POS-tagged corpus of Irish tweets and the training of statistical POS-tagging models. We show how existing resources can be leveraged for this domain-adapted resource development.