They claim they use the Axolotl double ratchet, though Moxie/OWS claims Wire uses a variation of the protocol they don't recommend.
[1] https://news.ycombinator.com/item?id=12148728
[2] https://news.ycombinator.com/item?id=12361410
[3] https://hn.algolia.com/?query=%22wire%20does%20not%20use%22%...
[4] (long but enlightening read) https://news.ycombinator.com/item?id=11725602
4 days ago, no follow-ups to questions for details.
...and which most of my friends used.
I'm OK with Signal's UX, but the problem is that I know exactly two people who use it too, everyone else is on WhatsApp. I mean: Writing this implementation would be hard, but still tremendously easier than getting enough traction to make it useful.
However it's hard to recommend because of the lack of features.