Neutron stars are the densest material objects in the universe, and the properties of these stars are determined by the strong, weak, electromagnetic, and gravitational forces.

A long-standing goal in astrophysics and nuclear particle physics has been to determine the neutron star equation of state, which could reveal the existence of new, exotic states of matter deep inside the star.

A neutron star in a binary is deformed by the gravitational field of its companion, and the extent to which the star is tidally deformed is determined by its equation of state.

I review how gravitational wave measurements of the orbit of two neutron stars provides a powerful way to study those stars tidal deformability, which in turn can be used to study the neutron star equation of state.

I then discuss recent work which shows that gravitational wave measurements of the tidal deformability can additionally provide a window into the non-equilibrium, dissipative properties of neutron star matter, which sheds light on the relative important of weak interactions within the neutron star core.