  We consider primordial black hole (PBH) production in inflationary
$\alpha$-attractors. We discuss two classes of models, namely models with a
minimal polynomial superpotential as well as modulated chaotic ones that admit
PBHs. We find that a significant amplification of the curvature power spectrum
${\cal P_R}$ can be realized in this class of models with a moderate tuning of
the potential parameters. We consistently examine the PBH formation during
radiation and additionally during reheating eras where the background pressure
is negligible. It is shown that basic features of the curvature power spectrum
are explicitly related with the postinflationary cosmic evolution and that the
PBH mass and abundance expressions are accordingly modified. PBHs in the mass
range $10^{-16}-10^{-14} \, M_{\odot}$ can form with a cosmologically relevant
abundance for a power spectrum peak ${\cal P_R} \sim 10^{-2}$ and large
reheating temperature and, furthermore, for a moderate peak ${\cal P_R} \sim
10^{-5}$ and reheating temperature $T_\text{rh}\sim 10^7$ GeV, characteristic
of the position of the power spectrum peak. Regarding the CMB observables, the
$\alpha$-attractor models utilized here to generate PBH in the low-mass region
predict in general a smaller $n_s$ and larger $r$ and $\alpha_s$ parameter
values compared to the conventional inflationary $\alpha$-attractor models.
