In spite of popular myth, most modern “broncs” are not in fact wild horses, but are more commonly spoiled riding horses or horses bred specifically as bucking stock.

Bronc riding – there are two divisions in rodeo, bareback bronc riding, where the rider is only allowed to hang onto a bucking horse with a surcingle, and saddle bronc riding, where the rider is allowed a specialized western saddle without a horn (for safety) and may hand onto a heavy lead rope attached to a halter on the horse.

Bull Riding – though technically not an equestrian event, as the cowboys ride full-grown bulls instead of horses, skills similar to bareback bronc riding are required.

(Source:Wikipedia.org)