Imagine something like: A deep network reduces a 20 page document to a summary of 4 or 5 sentences, you can click on these sentences to "expand" them out, eventually getting to the original text. Saving them from reading the whole document
A separate classifier automatically classifies the document into one of say, 20 categories (or whatever is appropriate).
A Deep Learning named entity recogniser extracts the Human names, Dates and times, Email addresses, Company Names, email addresses, Money amounts, and numbers from each document, then off to elasticsearch for indexing and easy searching.
Then we can start to play with higher level legal concepts that (for example) set precedent, or search for certain logical fallacies. (the next step past machine learning is machine reasoning - and it's starting to be possible now)