  In this review article, we argue that our current understanding of the
thermodynamic properties of cold QCD matter, originating from first principles
calculations at high and low densities, can be used to efficiently constrain
the macroscopic properties of neutron stars. In particular, we demonstrate that
combining state-of-the-art results from Chiral Effective Theory and
perturbative QCD with the current bounds on neutron star masses, the Equation
of State of neutron star matter can be obtained to an accuracy better than 30%
at all densities.
