  How does subatomic matter organize itself? Neutron stars are cosmic
laboratories uniquely poised to answer this fundamental question that lies at
the heart of nuclear science. Newly commissioned rare isotope facilities,
telescopes operating across the entire electromagnetic spectrum, and ever more
sensitive gravitational wave detectors will probe the properties of
neutron-rich matter with unprecedented precision over an enormous range of
densities. Yet, a coordinated effort between observation, experiment, and
theoretical research is of paramount importance for realizing the full
potential of these investments. Theoretical nuclear physics provides valuable
insights into the properties of neutron-rich matter in regimes that are not
presently accessible to experiment or observation. In particular, nuclear
density functional theory is likely the only tractable framework that can
bridge the entire nuclear landscape by connecting finite nuclei to neutron
stars. This compelling connection is the main scope of the present review.
