Yoga — like other mind-body exercises such as tai chi and meditation — seems to be particularly helpful at reducing harmful inflammation. A 2014 meta-analysis on the effects of mind-body therapies on the immune system found that yoga reduces inflammation-based blood markers. So did this 2014 randomized control trial looking at women with breast cancer and breast cancer survivors.
Michael Irwin at UCLA's medical school, one of the authors of a 2015 descriptive review on inflammation and mind-body exercises, said, "When you look at the aerobic exercise necessary to decrease inflammation, people have to maintain very vigorous levels." But not with yoga, he continued. "Even practices with minimum levels of physical activity [like Iyengar stretches] can have large effect sizes." Researchers don't yet know why, though they think the meditative components of yoga, tai chi, and meditation may have something to do with it.
I read a quote from the Saracens (I think?) rugby coach about the players doing yoga twice a week as part of their training. He said that regularly spending over an hour breathing deeply has to have a beneficial neurological and physical effect and I think he's probably right, whether tied in with the meditation aspect or not. They certainly noted the players' recovery from games/hard training was faster and injuries reduced after yoga was introduced.