Dependency Parsing seems to be present in most of the NLP toolkits out there.
What is not clear and what I have trouble finding in Google is what are actual practical, or even research, applications of parsing.
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Parsing is mostly an important building block used for improving the performance of downstream tasks, not as an application per se.
So, for example, if we are training NER, it helps to hint to the model what the parser guesses the noun phrases are. Similar for dialogue systems, translation and so on. See also: POS language model.
In the old days (before 2015 or so) parsing was typically an early step in a pipeline. Nowadays with end-to-end models it could be used to create the representation, either by marking up the text before vectorising, or as an additional vector. But anecdotally I can say that in the early days of deep learning mania raw text vector input had a lot of appeal, now we are in a phase of adding back a few of the things like parse trees and parts of speech.
Intuitively, the point is: a good parsing model has been trained on very large datasets, so your model can effectively incorporate all that knowledge of the world, for an aspect of language that generalises reasonably well across a language.