  Recent gravitational wave (GW) observations of binary black hole (BH) mergers
and the stochastic GW background have triggered renewed interest in primordial
black holes (PBHs) in the stellar-mass ($\sim 10 - 100\ \rm M_\odot$) and
supermassive regimes ($\sim 10^7 - 10^{11}\ \rm M_\odot$). Although only a
small fraction ($\lesssim 1\%$) of dark matter (DM) in the form of PBHs is
required to explain such observations, these PBHs may play important roles in
early structure/star/galaxy formation. In this chapter, we combine
semi-analytical analysis and cosmological simulations to explore the possible
impact of PBHs on the formation of the first stars and galaxies, taking into
account two (competing) effects of PBHs: acceleration of structure formation
and gas heating by BH accretion feedback. We find that the impact of
stellar-mass PBHs (allowed by existing observational constraints) on primordial
star formation is likely minor, although they do alter the properties of the
first star-forming halos/clouds and can potentially trigger the formation of
massive BHs, while supermassive PBHs serve as seeds of massive structures that
can explain the apparent overabundance of massive galaxies in recent
observations. Our tentative models and results call for future studies with
improved modeling of the interactions between PBHs, particle DM, and baryons to
better understand the impact of PBHs on early star/galaxy/structure formation
and their imprints in high-redshift observations.
