Realistic global neutron star models require numerical approach. Here, we briefly motivate and
recall the general-relativistic framework for the description of rotating compact stars and show
how global observable quantities can be computed unambiguously. Then, we present some recent
results on the building of more detailed physical models, including realistic microphysics, fol-
lowing two directions. First, we describe the inclusion of magnetic field and its effects on both,
global equilibrium and equation of state, and finally we discuss superfluid (two-fluid) models in
an attempt to model glitch phenomena.