Abstract: Gravitational waves provide a completely new way to study the universe. From the initial direct detection of coalescing black holes in 2015, to the ground-breaking multimessenger observations of coalescing neutron stars in 2017, and continuing with the now routine detection of merging stellar remnants, gravitational wave astronomy has quickly matured into a key aspect of modern physics. I will discuss novel tests of fundamental physics they enabled. In particular, I will focus on our current understanding of matter effects during the inspiral of compact binaries and matter at supranuclear densities, including possible phase transitions, through tests of neutron star structure. Detailed knowledge of dynamical interactions between coalescing stars, observations of extreme relativistic astrophysical systems, terrestrial experiments, and nuclear theory provide complementary views of fundamental physics. I will show how combining aspects from all these will improve our understanding of dense matter and the most extreme environments in the universe.