If you receive a ton of Direct Messages on Twitter, you might find it more than a little exasperating to scroll through them all to find one particular exchange. Thankfully, it seems that Twitter is working on improving its relatively bare bones UI for DMs in this regard.
According to prolific social media leakster Jane Manchun Wong, Twitter has started adding code to its web app that would allow one to search through past messages based on their recipient or the group chat they were part of. That's still not as functional as, say, Messenger, where you can also search based on the content and text of messages, rather than just who was on the other side of the conversation.
Wong noted that Twitter was also working on improving the filtering of messages by relegating spam to an "Additional Messages" tab, akin to Messenger's automatic sorting of messages it considers spam to the "Requests" section.
The feature is still in an experimental stage at this point so you can't use it yourself. When - and if - it'll make its way to the public remains to be seen.