  In this conference-proceedings contribution, we review recent advances in
placing model-independent constraints on the properties of cold and dense QCD
matter inside neutron stars. In addition to introducing new bounds for the
Equation of State, we explain how these results may be used to make robust
statements about the physical phase of strongly interacting matter in the
centers of neutron stars of different masses. Our findings indicate that the
existence of quark-matter cores inside massive neutron stars appears to be a
very common feature of the allowed Equations of State, and should not be
considered an exotic or unlikely scenario.
