The relativistic SU(3) Chiral Mean Field (CMF) model was the first model developed with the intent of describing several systems, among which are the interior of neutron and proto-neutron stars. More specifically it is a non-linear realization of the sigma model which includes pseudo-scalar mesons as the angular parameters for the chiral transformation. Depending on the choice of degrees of freedom, it can include nucleons, hyperons, spin 3/2 (Delta) baryons, light quarks, free leptons and mesons. The model reproduces standard nuclear physical constraints, as well as astrophysical ones, such as massive neutron stars. The quark sector of the model was fitted to reproduce lattice QCD results at zero and small densities. The model results were found to be in agreement with perturbative QCD for the relevant astrophysical regime. Within the model, baryons and quarks are mediated by vector-isoscalar, vector- isovector, scalar-isoscalar, and scalar-isovector mesons (including strange quark- antiquark states). At low densities and/or temperatures, the nuclear liquid-gas first-order phase transition is reproduced. At high densities and/or temperatures, chiral symmetry is restored, which can be seen in a reduction of the effective baryon masses, and, if the quarks are included in the model, deconfinement takes place. Here, we present two different kinds of EoS. The first one is for cold chemically-equilibrated neutron stars. The second one is for matter out of equilibrium, such as the one created in particle collisions, supernova explosions and neutron star mergers, in which case we vary not only the density, but also the temperature and electric charge fraction.