  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.
