Target recurve bows are the type of bows used in the Olympic Games and also competition at all levels. Commonly these bows are modular with the riser (handle) and limbs (the parts that bend) able to be separated. This allows the bow to be upgraded as well as packed away.
Olympic archery bows will have sights, stabilizers and are shot with the fingers on the string. Competitive Barebow archery uses the same bow, however no sight is allowed in competition and there are limitations in the way the stabilizers are set up.
Here is Australia's Ryan Tyack in action at the World Indoor Championships with a Target Recurve bow made by WIAWIS.