Résumé : We have recently developed a series of accurately calibrated nuclear energy density functionals, fitted to essentially all atomic masses with amodel root mean square deviation now reduced to 0.5 MeV for our functional BSk27*. At the same time, these functionals were adjusted to realistic equations of state of neutron matter and were constrained to reproduce various properties of nuclear matter. Using BSk27*, we have calculated the internal constitution and the equation of state of the crust of non-accreting neutron stars.