Snaffle bridle : Is a basic equestrian bridle that carries one bit and usually has one set of reins. Despite the name, a snaffle bridle may be used not only with a snaffle bit, but also with almost any other type of single rein bits, including kimberwickes, gag bits, and single curb bits.
Pelham bridle: The Pelham is another English type equestrian bridle that carries a single bit, in this case a Pelham bit, but two sets of reins, one for snaffle action and one for curb action.
Gag bridle: a bridle with rounded cheekpieces that pass through the top and bottom holes in the bit ring of a gag bit and attach directly to the reins. Tension on the reins rotates the bit and slides it up the cheekpieces and into the corners of the lips Gag bridles have the potential for severe action. They are often seen in polo, rodeo speed events, and occasionally show jumping. They are not permitted in most other horse show competition. In polo, they are often used with double reins, in the same manner as a Pelham bridle.
Double bridle: Also called a Weymouth bridle, double bridles use two bits at once, a small snaffle called a bradoon and a curb or Weymouth bit, and require the use of two sets of reins. Double bridles are usually only seen used in upper level dressage, and for showing in certain other events that require formal attire and equipment.
Hackamore Bridle: A hackamore, put simply, is headgear that controls a horse via pressure points on the face, usually with a nosepiece instead of a bit. A hackamore is not the same thing as a halter, as a halter is primarily used for leading and tying up an animal. Bitless bridles are similar to hackamores, but some designs use different leverage principles for control. Hackamores and bitless bridles use a headstall with reins attached to some type of noseband or nosepiece. Various designs allow control and good communication to the horse and may, in some cases, be more comfortable to the horse, particularly a young animal or one with a mouth injury.