Martingales and Breastplates

 The two most common types of martingale, the standing and the running, are used to control the horse's head height, and to prevent the horse from throwing its head so high that the rider gets hit in the face by the horse's poll or upper neck. When a horse's head gets above a desired height, the martingale places pressure on the head so that it becomes more difficult or impossible to raise it higher
 The breastplates purpose is to keep the saddle from sliding back, and is most helpful on horses with large shoulders and a flat ribcage. It is also a safety feature, especially on cross-country, should a rider's girth or billets break, as she will have enough time to stop the horse and dismount before the saddle slipped off the animal's back or underneath its belly.