  Primordial black holes (PBHs) are supposed to form from the collapse of
over-densed regions generated by large scalar curvature perturbations in the
radiation dominated era. Despite decades of various independent observations,
the nature of dark matter (DM) remains highly puzzling. Recently, PBH DM have
aroused interest since they provide an attracting explanation to the merger
events of binary black holes discovered by LIGO/VIRGO and may play an important
role on DM. During the formation of PBH, gravitational waves will be sourced by
linear scalar perturbations at second-order, known as the scalar-induced
gravitational waves (SIGWs), which provides a new way to hunt for PBH DM. This
topic review mainly focus on the physics about SIGWs accompanying the formation
of PBH DM.
