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Neutron stars are the most compact astrophysical objects outside of black holes. The energy densities at the cores most likely exceed those reached in heavy-ion collision where ordinary hadronic matter melts into deconfined quark matter. This naturally raises the question: is there quark matter also in the centers of Neutron Stars? To address this question, I discuss how combination of first principles, microscopic (pQCD) calculations and astrophysical observations help us constrain the material properties of the Neutron Star cores.