Primordial black holes from inflation

Abstract It has now been widely accepted that many inflation models can account for the formation of primordial black holes (PBHs). In particular, it has been fully realized that the PBH formation depends crucially on the tails of the probability distribution function of the curvature perturbation. I will review some models of inflation that give rise to the PBH formation, and their observational implications, in particular, for the blossoming field of gravitational-wave cosmology.