Our understanding has changed so much from when I was in school. Back then we did bouncing stretches. Which we now know can cause micro-tears in the muscle. Then we were advised to do static stretches. Which when done gently does no harm and eventually leads to increased mobility, which is a good thing. Except timing is everything. First reality is that stretching is a terrible way to warm up. Warming up mean literally to warm up the muscle. Stretching doesn't do that. Stretching also creates a neuromuscular inhibitory response, which means your strength will be decreased in that muscle by as much as 30% for perhaps the next 30 minutes. Dang! Whatever you do, don't stretch like this before you want to perform well.
So stretching works best when the muscle has been warmed up and become more pliable. And that is after you've exercised, not before. The current wisdom is to do "dynamic stretching" before you exercise. And just what is "dynamic stretching?" As far as I'm concerned it's not stretching at all. It's jumping jacks or leg swings or butt kicks. Stuff to sort of get your system going and get your brain integrated with range of motion movements. That sounds great to me. I'm just not sure why they're calling that stretching.
Rollers have become THE fashionable way to stretch. There is a growing sense that rolling a muscle against a roller does a better job of loosening it than the old approach of pulling on the muscle.
And the benefits of stretching? Well range of motion is great. Although part of running is the elastic response of your muscles and tendons. I've seen people so flexible, I found myself whether they'd be able to run well. You can be overstretched as far as running goes. Does it prevent injuries? So far, there's no research that supports that theory. The studies that have been done to date did not show fewer injuries among the groups that stretched.
So, yes, I do stretch, but I must say I'm not sure how much good it's doing me.