The structure of neutron stars is determined by a competition between
gravity and the pressure of strong interactions, and therefore neutron stars
provide a macroscopic laboratory for QCD. The progress in the observational
side is very fast: masses of over 30 neutron stars have been measured
precisely and the estimates of radii are getting increasingly accurate. In
my talk, I will describe how we can understand these observations and make
predictions using a combination of low energy nuclear physics and
perturbative QCD.