Understanding Neutron Stars from Gravitational Wave Observations

The first detection of gravitational waves from a binary neutron star merger, GW170817, ushered in a new era of neutron star studies. In the years since, observations of gravitational waves from merging neutron star systems -- containing either two neutron stars or a neutron star and a black hole – have provided new methods for probing neutron stars, through the measurement of their masses and tidal deformabilities. In this talk, I will give a broad review of what these measurements reveal about neutron star structure and the dense-matter equation of state, as well as the mass distribution of merging neutron stars. I will place these results in the context of other astrophysical constraints, and I will conclude by highlighting some exciting prospects for the next ten years of gravitational wave astronomy.