At speeds above 300-350 km/h, the main source of noise from trains is the aerodynamic noise caused by the air flow over the train structure. The sound level increases with train speed at a rate of between 60 and 80 times the logarithm of the speed so that, as speeds increase further, the noise increases dramatically. The main aerodynamic noise is produced by the air flow passing over the pantograph, the train nose, the bogie region and cavities such as the pantograph recess and the inter-coach gap. Experimental and numerical methods for studying aerodynamic noise are reviewed including the use of microphone arrays, wind tunnels, computational fluid dynamics and semi-empirical methods. Potential mitigation measures that can control aerodynamic noise are also reviewed.