  In this review article we discuss selected developments regarding the role of
the equation of state (EOS) in simulations of core-collapse supernovae. There
are no first-principle calculations of the state of matter under supernova
conditions since a wide range of conditions is covered, in terms of density,
temperature and isospin asymmetry. Instead, model EOS are commonly employed in
supernova studies. These can be divided into regimes with intrinsically
different degrees of freedom: heavy nuclei at low temperatures, inhomogeneous
nuclear matter where light and heavy nuclei coexist together with unbound
nucleons, and the transition to homogeneous matter at high densities and
temperatures. In this article we discuss each of these phases with particular
view on their role in supernova simulations.
