Draw reins and Running reins ( Draw reins are fitted between the legs - Running reins are fitted either side of the saddle )
In the correct hands they can be a good training aid BUT
Most people are not experienced enough to use them properly - in the wrong hands they can be the worst thing you could use. I have never used them and I never shall.
My point of view is that they teach the horse very little - in most cases if you give a horse something to fight against - that's what you will get, a fight.
If you are having trouble encouraging your horse to bring it's head down and need to resort to a piece of kit to do so - use a Market Harborough .
This will help bring the head down , when fitted correctly the downwards pressure will stop when the horse is in the correct position so a horse can learn that when a certain point is reached there is no more downwards pressure - you don't get this relief with draw reins.
The Market Harborough is out of fashion and is bad mouthed by a lot of people who don't know what they are talking about.