The detection of gravitational waves from binary black hole and binary neutron star mergers is opening new avenues for astrophysics and cosmology. I will talk about three different applications of gravitational waves in this regard. First, I will describe searches for post-merger gravitational waves following the binary neutron star merger GW170817, and search and inference methods I developed targeting such signals. On the cosmological front I will describe how gravitational wave detections can be used as tracers of the large-scale structure of the Universe, and techniques I have developed to use BBH detections by LIGO-Virgo for a statistical measurement of the structure. Finally, I will talk about Bayesian techniques I have developed to map the gravitational-wave sky with the upcoming space-based gravitational-wave detector LISA, focusing in particular on the galactic foreground from white dwarf binaries.