We are in an era in which we can observe gravitational waves from merging compact objects, an achievement that has taken a century to realize after the inception of Einstein's Theory of General Relativity. Neutron-star mergers make up an important subpopulation of such events because of their multimessenger signatures, their role in the origin of heavy elements, their implications for physics at supranuclear densities, and more. In order for two neutron stars to merge within the age of the Universe, a number of binary stellar interactions are necessary as two widely separated massive stars evolve toward a remnant double neutron star at close separations. I will focus on a particular phase of binary evolution in which a neutron star inspirals within the envelope of its companion massive star. Here, we model the evolution of this system while self-consistently accounting for the neutron star's strong gravity and the uncertainty on its interior equation-of-state. I will also discuss how our knowledge of the nuclear equation-of-state is improving as we continue to observe neutron stars with gravity and light.
