Modelling neutron stars is a complex task which depends on many ingredients, among others the properties of dense matter. In this talk I will discuss models of dense matter, relevant for the description of core-collapse supernovae, neutron stars and neutron star mergers. Such models have to cover large ranges in baryon number density, temperature and the particle composition. 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. I will highlight some implications for compact star astrophysics. In particular, after the first detection with gravitational waves (GW170817) and the associated electromagnetic signal, I will discuss relevant microphysics for a binary neutron star merger.