Equations of State for Neutron Stars and Core-collapse Supernovae

Modelling compact stars is a complex task which depends on many ingredients, among others the properties of dense matter. In this contribution models for the equation of state (EoS) of dense matter will be discussed, relevant for the description of core-collapse supernovae, compact stars and compact star mergers. Such EoS models have to cover large ranges in baryon number density, temperature and isospin asymmetry. The characteristics of matter change dramatically within these ranges, from a mixture of nucleons, nuclei, and electrons to uniform, strongly interacting matter containing nucleons, and possibly other particles such as hyperons or quarks. Some implications for compact star astrophysics will be highlighted, too.