A forefront 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 small as about 10 −22 s. 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.