Advances in experimental nuclear techniques have allowed for the production rarer and rarer short-lived isotopes, with extreme neutron-to-proton ratios. These represent unique testbeds for nuclear theorists, who try to understand and predict the properties of these exotic nuclei with a minimal set of ingredients. I will briefly review the interface between experiment and theory in present-day nuclear physics, with emphasis on some of the latest, unexpected phenomena observed in newly-produced isotopes. In addition to phenomenological methods, I will also discuss "ab initio" quantum many-body calculations, which provide a route to connect QCD to the equation of state as well as other observables in neutron-star matter.