  In this contribution, I discuss the utility that perturbative QCD offers in
studying the matter in the cores of neutron stars. I discuss the reasons why
perturbative QCD can constrain the equation of state at densities far below the
densities where we can perform controlled calculations. I discuss how
perturbative QCD can inform nuclear modelling of neutron stars and how it
influences equation-of-state inference. And finally, I discuss the implications
to the QCD phase diagram and argue that interesting features in the equation of
state revealed by the QCD input may be used to argue for the existence of
quark-matter cores in most massive neutron stars.
