Abstract: The observation of GW170817 realized the first <em<H</em<<sub<0</sub< measurement through the standard siren method, and initiated the era of standard siren cosmology. Ongoing gravitational wave observations of binary neutron star mergers are expected to measure <em<H</em<<sub<0</sub< within 2% accuracy in five years time, and to provide independent data to solve the <em<H</em<<sub<0</sub< tension. The third generation experiments will be able to accurately measure the expansion and structure growth rate of the universe over a wide redshift range, put stringent constraints on the nature of dark energy, and test general relativity on a cosmological scale.