Air traffic is growing at a steady rate of 3% to 5% per year in most regions of the world, implying a doubling every 15-25 years. This requires major advances in aircraft noise reduction at airports, just not to increase the noise exposure due to the larger number of aircraft movements. In fact it can be expected, as a consequence of increased opposition to noise by near airport residents, that the overall noise exposure will have to be reduced, by bans, curfews, fines, and other means and limitations, unless significantly quieter aircraft operations are achieved. The ultimate solution is aircraft operations inaudible outside the airport perimeter, or noise levels below road traffic and other existing local noise sources. These substantial noise reductions cannot come at the expense of a degradation of cruise efficiency, that would affect not just economics and travel time, but would increase fuel consumption and emission of pollutants on a global scale. The paper reviews the: (i) current knowledge of the aircraft noise sources; (ii) the sound propagation in the atmosphere and ground effects that determine the noise annoyance of near-airport residents; (iii) the noise mitigation measures that can be applied to current and future aircraft; (iv) the prospects of evolutionary and novel aircraft designs towards quieter aircraft in the near term and eventually to operations inaudible outside the airport perimeter. The 20 figures and 1 diagram with their legends provide a visual summary of the review.