The most accurate form of bow yet developed; in competions the 'unlimited' style of archery using this bow allows you to use a magnified sight, release aid (a trigger, the string is not held by the fingers), stabilisation, and a spirit level. Target shooting competions can lead to a tie at the shorter ranges; at the top level of performance.
A compound bow is similar to a recurve bow except a system of pulleys and cams is mounted at the end of the limbs of the bow. When the string of the bow is pulled back past a certain point the cams 'roll over' and the pulley system goes into action, dropping the weight held by about 65%. Also the limbs of the bow are very much shorter than a recurve (which means the mass to be accelerated upon release is reduced); coupled with the high draw weight of the bow, this leads to a much greater efficiency. Which in turn allows an archer to shoot an arrow farther and faster, and therefore the arrow has less time in the air to be affected by environmental conditions. Also as the archer isn't straining as much at full draw, the bow is easier to aim and so be again more accurate.
This is the type of bow most often used in bow hunting, as to kill with a bow you have have to be very accurate and hit the animal in the heart or a major blood vessel. An arrow kills due to the cutting damage it does (unlike a bullet which kills with the shock wave), which much lessens your chances; or increases your need for accuracy. In the UK all bow hunting is illegal; due the difficulty getting a killing shot, and the commensurate likelihood of the animal suffering.