Understanding the properties of infinite nuclear matter has important implications on many branches of nuclear science: from the bulk properties of exotic nuclei to the equation of state of neutron star matter. After we have extended the self-consistent Green’s function (SCGF) theory to account for three-nucleon forces, it is now possible to make reliable predictions of nucleonic matter at both zero and finite temperatures and with full chiral interactions, a task that was not possible until some years ago. The talk will present the SCGF approach as a very convenient way to investigate microscopic and thermodynamical properties of nucleonic matter. I will show how the infinite matter symmetry energy is predicted employing saturating potentials, built to reproduce properties of light and medium-mass nuclei. Furthermore, we will see how the prediction of the liquid-gas phase transition critical temperature in symmetric matter appears to be in reasonable agreement with experimental outcomes. I will then conclude presenting first-principle tests of thermal approximations used in equations of state to study stellar environments, which questions the validity of such astrophysical simulations.