In 1992, Sir James Lighthill foresaw the dawn of a second golden age in aeroacoustics enabled by computer simulations (Hardin JC, Hussaini MY (eds) 1993 Computational aeroacoustics, New York, NY: Springer (doi:10.1007). This review traces the progress in large-scale computations to resolve the noise-source processes and the methods devised to predict the far-field radiated sound using this information. Keeping focus on aviation-related noise sources a brief account of the progress in simulations of jet noise, fan noise and airframe noise is given highlighting the key technical issues and challenges. The complex geometry of nozzle elements and airframe components as well as the high Reynolds number of target applications require careful assessment of the discretization algorithms on unstructured grids and modelling compromises. High-fidelity simulations with 200-500 million points are not uncommon today and are used to improve scientific understanding of the noise generation process in specific situations. We attempt to discern where the future might take us, especially if exascale computing becomes a reality in 10 years. A pressing question in this context concerns the role of modelling in the coming era. While the sheer scale of the data generated by large-scale simulations will require new methods for data analysis and data visualization, it is our view that suitable theoretical formulations and reduced models will be even more important in future.