  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.
