Having worked in e-discovery for many years, "exponential improvements" is a huge overstatement. What they have is in pretty much any e-discovery product on the market.
And they are missing a huge piece--predictive coding and advanced analytics (email threading and near-dup are EXTREMELY common). If you are in NLP, ML and/or IR, the legal industry is probably one of the most exciting places to be. Huge datasets, available annotators and tons of money. It's a red-hot lab of state of the art techniques being tried in the real world instead of on the Reuters, 20-newsgroups, Enron, and other "canned" datasets.
The other thing is that lawyers don't get re-trained. Relativity has won the current generation of lawyers, and Relativity is a good product (unlike the products it replaced, Concordance and Summation). It will not be easy to displace.
On the research end of things, NIST's TREC has a legal track, and that's probably the best place to look for what's happening in the "applied research" space of the field.
Any and everything to do with text analytics so that lawyers can find relevant documents faster. Concept searching (LSI, LDA, other topic models), query expansion, clustering, network analysis (emails), etc.
And they are missing a huge piece--predictive coding and advanced analytics (email threading and near-dup are EXTREMELY common). If you are in NLP, ML and/or IR, the legal industry is probably one of the most exciting places to be. Huge datasets, available annotators and tons of money. It's a red-hot lab of state of the art techniques being tried in the real world instead of on the Reuters, 20-newsgroups, Enron, and other "canned" datasets.