Neutron stars contain the largest reservoirs of degenerate fermions, reaching the highest densities we can observe in the cosmos, and probe matter under conditions that cannot be recreated in terrestrial experiments. Throughout the Universe, a large number of high-energy, cataclysmic astrophysical collisions of neutron stars are continuously occurring. These collisions provide an excellent testbed to probe the properties of matter at densities exceeding the density inside atomic nuclei, are an important site for the production of elements heavier than iron, and allow for an independent measurement of the expansion rate of our Universe.
To understand these remarkable events, reliable nuclear-physics input is essential. In this colloquium, I will review how to use state-of-the-art nuclear-physics calculations to provide a consistent and systematic approach to strongly interacting systems from nuclei to neutron stars with theoretical uncertainties. I will discuss nuclear-physics predictions for the dense nucleonic matter relevant for neutron stars, and discuss how astrophysical multi-messenger observations of neutron stars and their mergers can be used to further elucidate the properties of matter under extreme conditions.