The equation of state of neutron star matter and the symmetry energy

We present an overview of microscopical calculations of the Equation of State (EOS) of neutron matter performed using Quantum Monte Carlo techniques. We focus to the role of the model of the three-neutron force in the high-density part of the EOS up to a few times the saturation density. We also discuss the interplay between the symmetry energy and the neutron star mass-radius relation. The combination of theoretical models of the EOS with recent neutron stars observations permits us to constrain the value of the symmetry energy and its slope. We show that astrophysical observations are starting to provide important insights into the properties of neutron star matter.