The interest in primordial black holes (PBHs) has recently risen up 
again after the discovery of around 30 solar mass black holes through 
the LIGO/Virgo gravitational wave events. PBHs are black holes produced 
by gravitational collapse of the over-dense region in the early universe.
 An attractive origin of the overdensity is primordial perturbations 
generated during inflation. In this talk, I will first explain the 
relation between the power spectrum of the perturbations predicted by 
inflation models and the estimated PBH abundance. This relation has 
various theoretical uncertainties including the choice of the window 
function (https://arxiv.org/abs/1802.06393). Next, as a concrete model, 
I will briefly introduce the so-called axion-like curvaton model, where 
the phase direction of a complex scalar field different from inflaton is 
responsible for small-scale perturbations (
https://arxiv.org/abs/1711.08956, https://arxiv.org/abs/1805.07757). We 
found that PBHs produced in this model can successfully reproduce the 
LIGO/Virgo gravitational wave events. Finally, I would like to discuss 
the case where a single-field inflaton potential has an inflection point.
 There, a slow-roll violation enhances quantum fluctuation. We should 
use stochastic inflation formalism since the quantum back reaction could 
become significant. However, stochastic inflation beyond slow-roll 
regimes is nontrivial and worth investigating by itself. I will show a 
numerical result obtained so far under a simplified setup.