Neutron-rich nuclei and the equation of state of stellar matter

In this contribution we will review our present understanding of the matter equation of state in the density and temperature conditions where it can be described by nucleonic degrees of freedom. At zero temperature, all the information is contained in the nuclear energy functional in its isoscalar and isovector channels. At finite temperature, particular emphasis will be given to the specificity of the thermodynamics in the nucleonic regime, with the simultaneous presence of long range electromagnetic and short range nuclear interactions. The astrophysical implications of the resulting phase diagram, as well as of different observables of exotic nuclei on the neutron-rich side, will be touched upon.