Quasinormal modes of perturbed black holes have recently gained much interest because of their tight relations with the gravitational wave signals emitted during the post-merger phase of a binary black hole coalescence. One of the intriguing features of these modes is that they respect the no-hair theorem, and hence, they can be used to test black hole space-times and the underlying gravitational theory. In this paper, we exhibit three different aspects of how black hole quasinormal modes could be altered in theories beyond Einstein general relativity. These aspects are the direct alterations of quasinormal modes spectra as compared with those in general relativity, the violation of the geometric correspondence between the high-frequency quasinormal modes and the photon geodesics around the black hole, and the breaking of the isospectrality between the axial and polar gravitational perturbations. Several examples will be provided in each individual case. The prospects and possible challenges associated with future observations will be also discussed.
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