Probing subatomic physics with gravitational waves from neutron star binary inspirals

The gravitational-wave signals from merging binary systems carry unique information about the internal structure of compact objects. This is of key interest for neutron stars, whose material is compressed by strong gravity to supra-nuclear densities where novel phases of matter emerge. I will discuss examples of recent progress in the theoretical modeling of gravitational-wave signatures resulting from the interplay of matter with strong-field gravity. I will also highlight insights gained from recent gravitational-wave discoveries, and conclude with an outlook onto the remaining challenges and exciting prospects for the next years, as gravitational-wave science continues to move towards an era of precision physics.