  In this paper we review the possible mechanisms for the production of
primordial black holes (PBHs) during a slow-reheating period {in which the
energy transfer of the inflaton field to standard model particles becomes
effective at slow temperatures}, offering a comprehensive examination of the
theoretical foundations and conditions required for each of formation channel.
In particular, we focus on post-inflationary scenarios where there are no
self-resonances and the reheating epoch can be described {by the inflaton
evolving in} a quadratic-like potential. In the hydrodynamical interpretation
of this field during the slow-reheating epoch, the gravitational collapse of
primordial fluctuations is subject to conditions on their sphericity, limits on
their spin, as well as a maximum velocity dispersion. We show how to account
for all conditions and show that PBHs form with different masses depending on
the collapse mechanism. Finally we show, through an example, how PBH production
serves to probe both the physics after primordial inflation, as well as the
primordial powerspectrum at the smallest scales.
