  We present the evolution of black holes (BHs) and their relationship with
their host galaxies in Astrid, a large-volume cosmological hydrodynamical
simulation with box size 250 $h^{-1} \rm Mpc$ containing $2\times5500^3$
particles evolved to z=3. Astrid statistically models BH gas accretion and AGN
feedback to their environments, applies a power-law distribution for BH seed
mass $M_{\rm sd}$, uses a dynamical friction model for BH dynamics and executes
a physical treatment of BH mergers. The BH population is broadly consistent
with empirical constraints on the BH mass function, the bright end of the
luminosity functions, and the time evolution of BH mass and accretion rate
density. The BH mass and accretion exhibit a tight correlation with host
stellar mass and star formation rate. We trace BHs seeded before z>10 down to
z=3, finding that BHs carry virtually no imprint of the initial $M_{\rm sd}$
except those with the smallest $M_{\rm sd}$, where less than 50\% of them have
doubled in mass. Gas accretion is the dominant channel for BH growth compared
to BH mergers. With dynamical friction, Astrid predicts a significant delay for
BH mergers after the first encounter of a BH pair, with a typical elapse time
of about 200 Myrs. There are in total $4.5 \times 10^5$ BH mergers in Astrid at
z>3, $\sim 10^3$ of which have X-ray detectable EM counterparts: a bright kpc
scale dual AGN with $L_X>10^{43}$ erg/s. BHs with $M_{\rm BH} \sim 10^{7-8}
M_{\odot}$ experience the most frequent mergers. Galaxies that host BH mergers
are unbiased tracers of the overall $M_{\rm BH} - M_{*}$ relation. Massive
($>10^{11} M_{\odot}$) galaxies have a high occupation number (>10) of BHs, and
hence host the majority of BH mergers.
