  Does deconfined cold quark matter occur in nature? This is currently one of
the fundamental open questions in nuclear astrophysics. In these proceedings, I
review the current state-of-the-art techniques to address this question in a
model-agnostic manner, by synthesizing inputs from astrophysical observations
of neutron stars and their binary mergers, and first-principles calculations
within nuclear and particle theory. I highlight recent improvements in
perturbative calculations in asymptotically dense cold quark matter, as well as
compelling evidence for a conformalizing transition within the cores of massive
neutron stars.
