  Neutron stars are cosmic laboratories to study dense matter in Quantum
Chromodynamics (QCD). The observable mass-radius relations of neutron stars are
determined by QCD equations of state, and can reflect the properties of QCD
phase transitions. In the last decade there have been historical discoveries in
neutron stars, the discoveries of two-solar mass neutron stars and neutron star
merger events, which have imposed tight constraints on equations of state.
While a number of equations of state are constructed to satisfy these
constraints, a theoretical challenge is how to reconcile those constructions
with the microphysics expected from the hadron physics and in-medium
calculations. In this short article we briefly go over recent observations and
discuss their implications for dense QCD matter, referring to QCD constraints
in the low and high density limits, QCD-like theories, and lattice QCD results
for baryon-baryon interactions.
