Various methods to study the ground state of neutron star matter are compared and the corresponding neutron star models are contrasted with each other. In the low density region rho<10^14 gr cm^-3 the nuclear gas is treated here by means of a Thomas Fermi method and the nuclei are described by the droplet model of Myers and Swiatecki. For rho<10^14 gr cm^-3 both standard Brueckner theory with more realistic interaction ( one-boson-exchange ) potentials and the semiphenomenological theory of Fermi liquids ( together with the standard Reid softcore potential ) are applied to neutron star matter. It is shown that while the high mass limit of neutron stars is hardly affected, some properties of lowmass neutron stars such as their binding depend sensitively on these refinements. Various tentative ( but unreliable ) extensions of the equation of state into high density regime rho>10^15 gr cm^-3 are investigated and it is shown that the mass limit for heavy neutron stars lies around 2.5 solar masses. It is further shown that a third family of stable ( hyperon ) stars is not forbidden by general relativistic arguments if there is a phase transition at high densities.