We study the properties of dense, strongly interacting matter using the Dyson–Schwinger equation (DSE) formalism. Within this formalism, by using particular sets of truncations, one can self–consistently derive quark properties in–medium. No first principle calculations of QCD are able to provide reliable results for such conditions. The effective models used instead, most notably the Nambu–Jona-Lasino and tdBag models can be understood as limiting cases of the DSE. Furthermore, the formalism provides a straightforward method for extending the derived models to finite temperature and isospin asymmetry, making them useful for studies of astrophysical phenomena such as core–collapse supernovas, neutron star mergers and in general to derive neutron star properties. We will focus on the current state–of–the–art in DSE studies of these phenomena.