Understanding the host galaxy properties of stellar binary black hole
(SBBH) mergers is important for revealing the origin of the SBBH gravitational
wave sources detected by advanced LIGO and Virgo and also helpful for identifying
their electromagnetic counterparts. In this talk, I will report our investigations
on the properties of the host galaxies of SBBHs by implementing simple recipes for
SBBH formation and mergers into cosmological galaxy formation models. We find
that SBBH mergers with total mass M_tot >= 10 M_sun$ at redshift z <~0.3 occur
preferentially in big galaxies with stellar mass >10^{10} M_sun; while the host
galaxy stellar mass distribution of heavy SBBH mergers with M_tot >~ 50 M_sun,
similar to GW150914, GW170104, and GW170814, is probably bimodal with one peak
at ~ 10^9 M_sun and the other peak at ~2 X 10^{10} M_sun. If SBBHs were formed
at early time (e.g., z>6; or from Pop III stars), their mergers detected at z
<~ 0.3 occur preferentially in even more massive galaxies with stellar mass >~
3 X 10^{10} M_sun. Although heavy SBBHs should have been formed mostly in small
galaxies with metallicities <~ 0.2 Z_sun, their host galaxies at the SBBH merger
time have substantially higher metallicities, peaking around 0.5 -0.6 Z_sun. I will
also talk about the clustering and other statistical properties of those GW sources.