I'm actually working on something simmiliar with a friend of mine, you send us a link of an article you don't want to read because it's to long and we summarize it for you in 3 sentences.
a summarizer. This is a field of NLP/NLU. Do you prefer to extract key phrases or a realy summary that extract important notions and rephrase it. Take a look a sumy for an overview.
I believe "extract notions and summarizing" is what will be more useful. Also I believe achieving this would give us much better search inside chats. This should be totally possible with the current state of NLP we have.
Just lazy to do it myself ;)