The scientific support of compression lends itself more towards the biomechanics of the athlete, improving joint support etc, but from a recovery and physical performance point of view the evidence is rather lightweight .
There are loose claims of improvement from a recovery standpoint, but the evidence is hypothetical and the claims are empirical. There’s always a placebo effect that can bias a study of course, but until the mechanisms by which compression garments work are entirely clear and proven, it remains a technology with slightly dubious claims – very little of the evidence in the meta-analysis showed any significant performance improvement across either endurance or resistance exercise.
There are cases where blood flow improvement is recorded  by compression garments, but these aren’t associated with dramatic improvements in performance within the same study. This may be down to the nature of the improvement of blood flow.
Meta-analysis  also shows that there may be some post-exercise recovery benefits, but they aren’t as strong as the infrared. In terms of sporting improvements the results aren’t significant, but there was evidence of strength improvement – this is likely down to the compressive nature of the clothing helping the athletes with strength movements due to biomechanical support.
The lack of sporting improvement is further evidence by this study involving compression garments and cyclists , where compression was said to have a ‘trivial’ improvement on power output, but no difference on blood lactate or perceived soreness.