  Motivated by recent detections of black hole binary systems through
gravitational waves, in this thesis we discuss two complementary channels for
the observation of Primordial Black Holes (PBHs) with masses between a few and
a hundred solar masses. First, we consider the possibility of detecting black
holes in the Milky Way through the electromagnetic radiation emitted in the
process of gas accretion, separately examining the astrophysical black hole
population and an hypothetical primordial one. We employ a state-of-the-art
accretion model, able to account for radiative feedback. Our findings suggest
that the detection of astrophysical isolated black holes in the vicinity of the
galactic center is around the corner. We perform a complete parametric study of
the uncertainty associated with this prediction. We then turn to constraining
PBH abundance through the same channel, finding that existing bounds can be
significantly relaxed when modelling uncertainties are taken into account. The
PBH mass function motivated by the Universe's thermal history is considered. In
the second part, we turn to gravitational wave observations. The possibility of
disentangling the astrophysical background form a possible primordial signal in
present data is hampered by large theoretical uncertainties on the properties
of both populations. However, third-generation gravitational wave detectors
will be able to detect mergers up to the dark ages, where the astrophysical
background is expected to be absent. Through mock data generation and analysis,
we assess the ability of the Einstein Telescope (ET) to identify a subdominant
population of PBHs, disentangling it from the astrophysical one based
exclusively on event distance measurements. We find that the ET should be able
to detect and constrain the PBH abundance if these constitute at least
approximately one part in $10^5$ of the dark matter.
