This contribution addresses recent advances in the prediction of aircraft noise, including the development of new numerical models and computational tools, supported by an increasing database of noise measurements at commercial airfields. The models and tools described in this contribution are aimed at the optimisation of operational procedures, the improvement in understanding in the causes of noise, the determination of noise maps at realistic airfields, and hence the reduction of noise annoyance from commercial aviation. Examples of comparisons between predictions and field measurements are given as well as noise footprints at London Heathrow. Effects of trajectory displacements are shown for takeoff and landings. Airplanes considered include the Airbus A320-211 and the Boeing B747-400. Gaps in knowledge of low-order methods for aircraft noise are discussed.