  One of the most compelling candidates for Dark Matter (DM) are light
pseudo-scalar particles (axions), motivated by the strong CP problem and
axiverse scenario in string theory. Depending on their mass and type of
self-interaction, these particles can build self-gravitating configurations
such as compact objects, DM clumps or even galactic DM halos. On the other
hand, superradiant instabilities can produce long-living extended
configurations (scalar clouds) gravitating around Black Holes (BHs). As these
scalars are real and harmonic, their interaction with the other matter
components can induce a parametric resonance that might lead to their
observable signatures. First, we consider the orbital dynamics of test
particles in these axion configurations, show when resonances can occur and
discuss the secular evolution of the orbital elements. This scenario can lead
to observable consequences for binary pulsars or S stars around the
supermassive BH in our Galaxy. Secondly, we discuss electromagnetic (EM) field
instabilities in homogeneous axion configurations as well as scalar clouds
around Kerr BHs. These axion-photon resonances can quench superradiant
instabilities, while producing an observable signature in the EM sector. We
give an analytical estimate of the rate of these processes that have good
agreement with the fully relativistic numerical simulations and discuss the
impact of plasma in the vicinity of BHs on these instabilities.
