  Primordial black holes (PBHs) may have left an imprint in the form of a
stochastic gravitational wave background (SGWB) throughout their evolution in
the history of the Universe. This review highlights two types of SGWB: those
generated by scalar curvature perturbations associated with PBH formation in
the early Universe and those composed of ensembles of GWs emitted by PBH
binaries. After describing detection methods and a brief introduction on
Bayesian inference, we discuss current constraints imposed by LIGO-Virgo-KAGRA
(LVK) observations through the non-detection of the SGWBs and discuss their
physical implications.
