I would say.... inconclusive.
I found this which is a compilation study on the studies of compression clothing specifically for runners:
https://www.ncbi.nlm.nih.gov/pubmed/27106555
In it they found that the sleeves main benefit is the raise in muscle temperature which they claim helps reduce post-leg soreness and muscle fatigue. They did not find any benefit in athletic performance, although reduced muscle fatigue will mean that you can run slightly faster or longer bursts.
Yet here is another article on the effects of DOMs and wearing compression clothing:
https://link.springer.com/article/10.1007/BF02214641#page-1
In it they conclude that there is no difference in both performance or DOMs when wearing compression clothing or not.
This one on the effects of compression clothing notes that there might be some reduction in perceived muscle soreness for some people though it seems to be small.
And this seems to be the theme for most of these studies.
The problem with studies like this is it's absolutely impossible to remove the placebo effect. You can't do a double blind study like you could with medicine. The positive effects may be because people believe it works.
From an athletes perspective, they want to give themselves every advantage they possibly can within the bounds of the rules of their sport. There is some evidence that compression clothing might help. Basketball and baseball hasn't banned compression clothing yet, so they wear compression clothing even though the science on it seems rather scant.
This is why a few years ago, it seems like everyone at the Olympics was wearing KT tape. This is why last year's Olympic fad was cupping. Neither had super-strong evidence supporting their usage at the time, but there was some so athletes used it.
EDIT:
Perceived recovery benefits aside. There are other reasons to consider compression gear. It doesn't get in the way like more baggy clothes. It's light. They tend to be very durable. It does help keep people warm which is important in the colder months. Compression clothing can just be comfortable to wear.