In this review article, we discuss selected developments regarding the role of the equation of state 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 equation of state 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.