I will discuss how current observations for neutron stars constrain QCD equations of state, from nuclear to quark matter domain. The 2 solar mass and recent trend of the radius determination together constrain the nature of QCD matter and the structure of QCD phase diagram; the observational constraints indicate the nature of QCD phase transition from hadronic to quark matter is likely to be a crossover or an weak first order. Using a schematic model inspired from hadron and nuclear physics, I will delineate properties of quark matter at density higher than 5 times nuclear saturation density. It is found that the quark matter in such density should be strongly correlated due to gluons with non-perturbative nature.