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In the last decade, many research groups have reported predictions of jet noise using high-fidelity large-eddy simulations (LES) of the turbulent jet flow and these methods are beginning to be used more broadly. A brief overview of the publications since the review of Bodony and Lele (2008, AIAA J., Vol. 56, 346-380) is undertaken to assess the progress and overall contributions of LES towards a better understanding of jet noise. In particular, we stress the meshing, numerical and modeling advances which enable detailed geometric representation of the nozzle shape variations intended to impact the noise radiation, and sufficiently accurate capturing of the turbulent boundary layer at the nozzle exit. Examples of how LES is currently being used to complement experiments for challenging conditions (such as highly heated pressure mismatched jets with afterburners) and guide jet modeling efforts are highlighted. Some of the physical insights gained from these numerical studies are discussed, in particular on crackle, screech and shock-associated noise, impingement tones, acoustic analogy models, wave packet dynamics and resonant acoustic waves within the jet core. We close with some perspectives on the remaining challenges and upcoming opportunities for future applications. This article is part of the theme issue `Frontiers of aeroacoustic research: theory, computation and experiment'.