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Black hole quasi-normal modes (QNMs) dominate the ringdown phase of the gravitational-wave signal following black hole binary mergers, and their precise measurement underpins black hole spectroscopy. In this talk, I will review recent progress in our understanding of the Green's function for spin-2 perturbations of a broad class of black hole spacetimes. I will then discuss how nonlinearities modify the ringdown through mode coupling and the excitation of second-order QNMs, before concluding with recent work exploring how astrophysical environments may shift QNM frequencies.