Recent advances in the understanding of turbofan noise generation and suppression in aircraft engines are reviewed with particular emphasis on NASA research. The review addresses each link in the chain of physical processes which connect unsteady flow interactions with fan blades to far field noise. Mechanism identification and description, duct propagation, radiation and acoustic suppression are discussed. Recent advances in the experimental technique of fan inflow control assure that in-flight generation mechanisms are not marked by extraneous sources in static tests. Rotor blade surface pressure and wake velocity measurements aid the determination of the types and strengths of the generation mechanisms. Approaches to predicting or measuring acoustic mode content, optimizing treatment impedance to maximize attenuation, translating impedance into porous wall structure and interpreting far field directivity patterns are illustrated by comparisons of analytical and experimental results. A persistent theme of the review is the interdependence of source and acoustic treatment design to minimize far field noise. Areas requiring further research are discussed and the relevance of aircraft turbofan results to quieting other turbomachinery installations is addressed.