The equation of state (EoS) of isospin asymmetric nuclear matter is a fundamental ingredient in the description of the static and dynamical properties of neutron stars, core-collapse supernova and compact-star mergers.

In this talk I will make a review of different experimental and astrophysical observational constraints of the nuclear EoS as well as of several phenomenological models and ab-initio theoretical many-body approches commonly used in the literature in its description.