The phases of QCD reached in terrestrial and cosmic colliders

We review the current state of knowledge of the phase diagram of QCD through lattice, effective field theories, and chiral models. Several sections through the three dimensional phase diagram are known for $N_f=2+1$ with good precision. Due to technical advances in lattice techniques over the last decade or so, new aspects of the phase diagram can now be explored. We review current lattice results. The newly acquired knowledge can be used to reconstruct the full phase diagram for physical QCD, \ie, $N_f=1+1+1$. We remark on the computations which would help understand this better, and what the current constraints are on matter in neutron star cores. We also remark on the physics of the chiral transition and neutron stars in the 't Hooft large $N_c$ limit.