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 talk, I will explain how to use quantum Monte Carlo calculations employing interactions from chiral effective field theory to provide a consistent and systematic approach to nuclei and neutron-star matter with controlled theoretical uncertainties. I will present results for atomic nuclei and nuclear-physics predictions for the equation of state of neutron stars, and discuss how multi-messenger observations of binary neutron-star mergers can be used to further elucidate the properties of matter under extreme conditions.