  During the next decade, gravitational waves will be observed from hundreds of
binary inspiral events. When the redshifts of the host galaxies are known,
these events can be used as `standard sirens', sensitive to the expansion rate
of the Universe. Measurements of the Hubble constant $H_0$ from standard sirens
can be done independently of other cosmological probes, and events occurring at
$z<0.1$ will allow us to infer $H_0$ independently of cosmological models. The
next generation of spectroscopic galaxy surveys will play a crucial role in
reducing systematic uncertainties in $H_0$ from standard sirens, particularly
for the numerous `dark sirens' which do not have an electromagnetic
counterpart. In combination with large spectroscopic data sets, standard sirens
with an EM counterpart are expected to constrain $H_0$ to $\sim 1-2\%$
precision within the next decade. This is competitive with the best estimates
of $H_0$ obtained to date and will help illuminate the current tension between
existing measurements. Information on the galaxies that host the gravitational
wave events will also shed light on the origin and evolution of compact object
binaries.
