A transition from normal hadronic matter (such as protons and neutrons) to quark-gluon matter is expected at both high temperatures and densities. In physical situations, this transition may occur in heavy ion collisions, the early universe, and in the cores of neutron stars. Astrophysics and cosmology can be greatly affected by such a phase transition. With regard to the early universe, big bang nucleosynthesis, the theory describing the primordial origin of the light elements, can be affected by inhomogeneities produced during the transition. A transition to quark matter in the interior by neutron stars further enhances our uncertainties regarding the equation of state of dense nuclear matter and neutron star properties such as the maximum mass and rotation frequencies.