In the last few years several interesting phenomena associated to the
interaction between massive black holes and fundamental bosonic fields
have been discovered. I present a selection of them, including
superradiance instabilities of spin-0, spin-1 and spin-2 fields,
floating orbits in extreme-mass ratio inspirals and black-hole
spontaneous scalarization. The theoretical potential of these effects
as almost-model-independent smoking guns for exotic particles and
modified gravity, as well as their limitations in realistic
astrophysical scenarios, are discussed.