Since the start of radio astronomy in the 1950s, astronomers have mapped
-in great detail- the neutral hydrogen of the local universe using 21cm
observations. However, current radio facilities limit these observations
to low redshift (z < 0.4). Above these redshifts, neutral hydrogen can
best be studied through absorption spectroscopy, whereby the HI imprints
an absorption signature in the light of a background source (often, but
not always, a quasar). Absorption spectroscopy allows us to accurately
determine the cosmic mass distribution of HI, but these observations are
unable to detemine what galaxies are associated with this HI.

In this talk, I will highlight some of the recent advancements in trying
to connect individual HI absorption systems with galaxies, in order to
try to understand what galaxies harbor the bulk of the gas in our
universe. In particular, I will highlight the transformative role ALMA
is having in detecting galaxies associated with HI absorption systems.
These recent detections corroborate previous assertions that the galaxy
populations responsible for the bulk of HI absorption is qualitatively
similar to the Lyman-break galaxy population, although with potentially
more molecular gas. Comparing the distribution of HI around the galaxy
shows that it extends well-beyond the star-forming regions of galaxies.
In some cases this gas is co-rotating with the disk, whereas in other
cases it seems to trace the circumgalactic medium of the galaxy. Most of
all, these observations show that with current facilities it is possible
to provide the first constraints of the HI distribution surrounding high
redshift galaxies.