Abstract This paper explores how to syntactically parse Ancient Greek texts automatically and maps ways of fruitfully employing the results of such an automated analysis. Special attention is given to documentary papyrus texts, a large diachronic corpus of non-literary Greek, which presents a unique set of challenges to tackle. By making use of the Stanford Graph-Based Neural Dependency Parser, we show that through careful curation of the parsing data and several manipulation strategies, it is possible to achieve an Labeled Attachment Score of about 0.85 for this corpus. We also explain how the data can be converted back to its original (Ancient Greek Dependency Treebanks) format. We describe the results of several tests we have carried out to improve parsing results, with special attention paid to the impact of the annotation format on parser achievements. In addition, we offer a detailed qualitative analysis of the remaining errors, including possible ways to solve them. Moreover, the paper gives an overview of the valorisation possibilities of an automatically annotated corpus of Ancient Greek texts in the fields of linguistics, language education and humanities studies in general. The concluding section critically analyses the remaining difficulties and outlines avenues to further improve the parsing quality and the ensuing practical applications.