  If primordial black holes of $\mathcal{O}(1-100) M_{\odot}$ constitute a
significant portion of the dark matter in the Universe, they should be very
abundant in our Galaxy. We present here a detailed analysis of the radio and
X-ray emission that these objects are expected to produce due to the accretion
of gas from the interstellar medium. With respect to previous studies, we relax
the assumption of a monochromatic mass function, and introduce an improved
treatment of the physics of gas accretion onto isolated, moving compact
objects, based on a set of state-of-the-art numerical simulations. By comparing
our predictions with known radio and X-ray sources in the Galactic center
region, we show that the maximum relic density of primordial black holes in the
mass range of interest is $\sim 10^{-3}$ smaller than that of dark matter. The
new upper bound is two orders of magnitude stronger with respect to previous
results, based on a conservative phenomenological treatment of the accretion
physics. We also provide a comprehensive critical discussion on the reliability
of this bound, and on possible future developments in the field. We argue in
particular that future multi-wavelength searches will soon start to probe the
galactic population of astrophysical black holes.
