  The properties of compact stars and their formation processes depend on many
physical ingredients. The composition and the thermodynamics of the involved
matter is one of them. We will investigate here uniform strongly interacting
matter at densities and temperatures, where potentially other components than
free nucleons appear such as hyperons, mesons or even quarks. In this paper we
will put the emphasis on two aspects of stellar matter with non-nucleonic
degrees of freedom. First, we will study the phase diagram of baryonic matter
with strangeness, showing that the onset of hyperons, as that of quark matter,
could be related to a very rich phase structure with a large density domain
covered by phase coexistence. Second, we will investigate thermal effects on
the equation of state (EoS), showing that they favor the appearance of
non-nucleonic particles. We will finish by reviewing some recent results on the
impact of non-nucleonic degrees freedom in compact star mergers and
core-collapse events, where thermal effects cannot be neglected.
