Models based on extended Thomas–Fermi and Strutinsky integral (ETFSI), Hartree–Fock + BCS (HFBCS) and Hartree–Fock–Bogolyubov (HFB) mean-field approximations with a phenomenological Skyrme functional, that are used in the calculation of atomic masses, are reviewed. The main physics content of these models is briefly described, both for finite nuclei and infinite nuclear matter. For finite nuclei, the discussion focuses on the treatment of deformation, odd-A and odd–odd nuclei, pairing and the correction for the Wigner anomaly. In infinite nuclear matter, the effective nucleon mass in nuclear matter and the symmetry energy and its density dependence are discussed. To further test the validity of the Skyrme functional parameter sets, deduced from fits to mass-data, the equation of state (EOS) for asymmetric beta-equilibrium nuclear matter is constructed. The EOS, supplemented at baryon number densities (0.08 > n_b > 0.00025) fm⁻³ by Baym–Bethe–Pethick (BBP) EOS and below that by Baym–Pethick–Sutherland (BPS) EOS, is used to predict maximum mass and radius of cold (T = 0) non-rotational neutron stars as well as the binding energy and radius of a 1.4M star. The present analysis has shown that there is no significant improvement either in the rms error of fit of the Hartree–Fock mass models to existing mass-data bases, or to new mass-data, with increasing sophistication of the models and the related number of fitting parameters. Further, the Skyrme functionals obtained from fits to nuclear masses cannot be successfully used in neutron-star models. This casts doubt on the suitability of these functionals for the description of neutron–heavy nuclei close to and beyond the neutron drip line. It is concluded that it is unlikely that the present HF mass models will ever yield atomic masses with the higher precision required by the r-process and related applications and a different approach to the calculation of masses should be sought.