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.
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