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Neutron stars are cosmic laboratories to study dense matter in QuantumChromodynamics (QCD). The observable mass-radius relations of neutron stars aredetermined by QCD equations of state, and can reflect the properties of QCDphase transitions. In the last decade there have been historical discoveries inneutron stars, the discoveries of two-solar mass neutron stars and neutron starmerger events, which have imposed tight constraints on equations of state.While a number of equations of state are constructed to satisfy theseconstraints, a theoretical challenge is how to reconcile those constructionswith the microphysics expected from the hadron physics and in-mediumcalculations. In this short article we briefly go over recent observations anddiscuss their implications for dense QCD matter, referring to QCD constraintsin the low and high density limits, QCD-like theories, and lattice QCD resultsfor baryon-baryon interactions.

QCD equations of state and speed of sound in neutron stars