  We give an overview about equations of state (EOS) which are currently
available for simulations of core-collapse supernovae and neutron star mergers.
A few selected important aspects of the EOS, such as the symmetry energy, the
maximum mass of neutron stars, and cluster formation, are confronted with
constraints from experiments and astrophysical observations. There are just
very few models which are compatible even with this very restricted set of
constraints. These remaining models illustrate the uncertainty of the uniform
nuclear matter EOS at high densities. In addition, at finite temperatures the
medium modifications of nuclear clusters represent a conceptual challenge. In
conclusion, there has been significant development in the recent years, but
there is still need for further improved general purpose EOS tables.
