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Thermoacoustic instability is a flow instability that arises due to a two-way coupling between acoustic waves and unsteady heat release rate. It can cause damaging, large-amplitude oscillations in the combustors of gas turbines, aeroengines, rocket engines, etc., and the transition to decarbonized fuels is likely to introduce new thermoacoustic instability problems. With a focus on practical thermoacoustic instability problems, especially in gas turbine combustors, this review presents the common types of combustor and burner geometry used. It discusses the relevant flow physics underpinning their acoustic and unsteady flame behaviors, including how these differ across combustor and burner types. Computational tools for predicting thermoacoustic instability can be categorized into direct computational approaches, in which a single flow simulation resolves all of the most important length scales and timescales, and coupled/hybrid approaches, which couple separate computational treatments for the acoustic waves and flame, exploiting the large disparity in length scales associated with these. Examples of successful computational prediction of thermoacoustic instability in realistic combustors are given, along with outlooks for future research in this area. [ABSTRACT FROM AUTHOR]