This happens in our house a lot. My boys are the same age, but one is a lot bigger and tends to be the "teaser" - he already knows the buttons to push and he pushes. Ds1 in turn screams and screetches and cries.
I don't purposely "let" natural consequences of not listening to ds1's request for ds2 to stop doing *something* happen, but they do happen many times since I am not right next to them at every moment. So, ds1 has been hitting a lot, after screaming for him to stop (for example). I talk to them separately, I tell ds1 he needs to keep using words, that if someone is not listening when you ask them to stop, that its ok to ask an adult to help, and that I liked the words he used, and that its frustrating when someone doesn't listen (etc) I tell ds2 that when he doesn't respond, and stop pulling, grabbing, teasing, etc sometimes kids can get frustrated and they may hit, and that its important for him to hear what his friends are saying, when they're asking to stop, also teasing someone hurts feelings... etc etc
I would also caution against suddenly "letting them work it out" completely on their own, depending on the age. I had a lot of frustration and hurt (emotional and physical) growing up between brothers, and I know they did too (I was the screamer, scratcher, etc). I do spend a lot of time with my boys "teaching" them to work it out, saying things like "oh, so you really want to play with this puzzle by yourself and your brother also wants to play with it all by himself... hm... that's a tough one, I wonder how we can work this out" and stay with them as its worked out. As it progresses, I just state that they need to work it out and see how it goes.
Another thing that has helped us with sharing, getting along, is finding really fun activities to do where they have to work together to complete it. Or just find those activities where they play really well together and talk about how nice it is to see them working things out, working together to figure things out, etc.
I will be very interested to hear what others have to say as this can get really frustrating at times and I can get to the point of yelling for peace and quiet.