Turbofan engines are one of the most popular propulsion systems used in commercial aircraft due to their high thrust and good fuel efficiency. To reduce noise generated from turbofan engines-powered aircraft, a number of control approaches have been developed. The dominant noise sources include the fan and the high-speed ‘hot’ and ‘cold’ jet. In engineering applications, the noise control approaches include: 1) active control, 2) geometric shape optimization, and 3) passive control (including acoustic boundary control). Because they are considered the most reliable and effective noise reduction methods, the geometric shape optimization and passive control are preferable by the engine manufacturers. In this work, we briefly overview the noise reduction technologies that have great potential to be applied or implemented on turbofan engines. The research and development progress made on the active control, passive control, and geometric shape optimization are reviewed and discussed, aiming to provide an useful guidance on next-generation low-noise turbofan engines. The fundamental noise damping mechanisms of thermos-viscous and vortex shedding are finally overviewed via cases studies.