  Recent developments in the theory of pure neutron matter and experiments
concerning the symmetry energy of nuclear matter, coupled with recent
measurements of high-mass neutron stars, now allow for relatively tight
constraints on the equation of state of dense matter. We review how these
constraints are formulated and describe the implications they have for neutron
stars and core-collapse supernovae. We also examine thermal properties of dense
matter, which are important for supernovae and neutron star mergers, but which
cannot be nearly as well constrained at this time by experiment. In addition,
we consider the role of the equation of state in medium-energy heavy-ion
collisions.
