Musicians generally use what's referred to as CIEM, or Custom In-ear Monitors. You get silicone squirted into your ear to get a mold of it and ship it to your company of choice and they'll hand craft you the monitors you've picked. That way they'll (hopefully) fit you perfectly when you're jumping around on stage and offer you great noise isolation to keep your ears safe.

Any one can obviously get these, I have a pair and I'm the farthest from a musician there is.

Sound quality wise they'll run the gamutm depends on how much money you want to spend. You can easily spend over $2k or as little as a few hundred.

Now you obviously don't have to go the custom route. That's just a niche market. IEM's are avalable from a few dollars to thousands upon thousands of dollars. As with everything there will be pros and cons when compared to regular headphones.