Flame-acoustic interactions are witnessed in the context of combustion instability in gas turbine combustors and other propulsion devices, such as rockets, besides confined combustion systems in general, such as furnaces and heaters. The confinement causes acoustic standing wave modes that interact with the flame to cause fluctuations in all quantities to grow in amplitude. This review categorizes the different canonical flame-holding geometries that mostly involve flow recirculation zones for flame stabilization, which are inherently unstable and feed into the flame-acoustic interaction cycle. The receptivity of the nonreacting shear layer to prevalent acoustic forcing in terms of development of coherent structures and instability of different hydrodynamic modes in the recirculation are detailed. The case of reacting flow instabilities involves several mechanisms of flame-acoustic coupling, such as vortex combustion; vortex-wall interactions; vortex-vortex interactions; flame area fluctuations and equivalence ratio, vorticity, and entropy fluctuations; bifurcations of the combustor dynamics; and its Strouhal scaling. In some instances, flame blowout dynamics as well as flashback are coupled with the prevalent acoustic oscillations. Some of these aspects have been well diagnosed in the recent literature, notably using planar laser-induced fluorescence for flame marking and particle image velocimetry to characterize the flow in a time-resolved manner. Reduced order models based on empirically determined flame transfer functions and predictive tools for onset of combustion instability based on time series analysis, either from a nonlinear dynamical viewpoint or a data-driven approach, are in current vogue.