Black holes are multifaceted objects that probe the strong-field nature of gravity and can be used to test fundamental physics. Astrophysical black holes may undergo superradiant instabilities in the presence of light bosonic fields. This effect, together with precision measurements of the mass and spin of massive black holes,has been used to constrain axions and ultralight scalars, to derive bounds on light vector fields and on the mass of the graviton, as well as to put intrinsic bounds on magnetic fields near black holes and on the fraction of primordial black holes in dark matter. The theoretical potential of these phenomena as almost-model-independent smoking guns for beyond-Standard Model physics and modified gravity are presented.