A forefront area of research concerns the exploration of the properties of hadronic matter under extreme conditions of temperature and density, and the determination of the equation of state-the relation between pressure, temperature and density-of such matter. Experimentally, relativistic heavy-ion collision experiments enable physicists to cast a brief glance at hot and ultra-dense matter for times as little as about 10 −22 seconds. Complementary to this, the matter that exists in the cores of neutron stars, observed as radio pulsars, X-ray pulsars, and magnetars, is at low temperatures but compressed permanently to ultra-high densities that may be more than an order of magnitude higher than the density of atomic nuclei. This makes pulsars superb astrophysical laboratories for medium and high-energy nuclear physics, as discussed in this paper.