Explore the use of gravitational waves in cosmology and the challenges of measuring the Hubble constant in this 43-minute conference talk by Rachel Gray from Queen Mary University of London. Delve into the concept of dark sirens and their potential to resolve the Hubble constant tension. Examine the Bayesian approach to cosmological parameter estimation using gravitational wave signals from compact mergers. Investigate the complexities of using galaxy catalogues for redshift information, including issues of incompleteness and the impact of gravitational wave population assumptions. Learn about the pixelation analysis technique and its effects on cosmological inferences. Discover the correlation between population and cosmological parameters, and review the latest cosmology results from GWTC-3.