What is the behavior of high-density, low-temperature QCD? At the high densities reached in the cores of neutron stars, this question becomes difficult to answer. In this talk, I will outline a framework to address this question, synthesizing inputs from nuclear theory, high-energy theory, and astrophysics. I will discuss how this framework can be used to constrain the degree of conformality of high-density QCD, with implications for the cores of high-mass neutron stars. I will furthermore highlight recent work to improve the perturbative-QCD input used in the framework.