  We consider several early Universe models that allow for production of large
curvature perturbations at small scales. As is well known, such perturbations
can lead to formation of primordial black holes (PBHs). We briefly review the
today's situation with PBH constraints and then focus on two models in which
strongly non-Gaussian curvature perturbations are predicted: the hybrid
inflation waterfall model and the curvaton model. We show that PBH constraints
on the values of curvature perturbation power spectrum amplitude are strongly
dependent on the shape of perturbations and can significantly (by two orders of
magnitude) deviate from the usual Gaussian limit ${\cal P}_\zeta \lesssim
10^{-2}$. We give examples of PBH mass spectra calculations for both
inflationary models.
