  The proper understanding of the equation of state (EoS) of highly asymmetric
nuclear matter is essential when studying systems such as neutron stars (NSs).
Using zero-range Skyrme interactions and finite-range interactions such as
Gogny forces, momentum-dependent interactions (MDI) and simple effective
interactions (SEI), we analyze the properties of the EoS and the influence they
may have on the calculations for NSs.
  We study the convergence properties of the Taylor series expansion of the EoS
in powers of the isospin asymmetry and the accuracy of the results for
$\beta$-stable nuclear matter when it is computed using the Taylor expansion of
the EoS. The NS mass-radius relation for Skyrme and finite-range interactions
is also analyzed. As none of the existing parametrizations of the standard
Gogny D1 interaction are able to provide an NS inside the observational
constraints, we propose a new parametrization, which we name D1M$^*$, that is
able to provide NSs of $2 M_\odot$ while still providing the same good
description of finite nuclei as D1M. A parametrization D1M$^{**}$ is also
presented, which is fitted similarly as D1M$^*$ and provides NSs up to $1.91
M_\odot$.
  An accurate determination of the core-crust transition point is necessary for
the modeling of NSs for astrophysical purposes. We estimate the core-crust
transition in NSs by finding where the nuclear matter in the core is unstable
against fluctuations of the density. To do that, we employ two methods, the
thermodynamical method and the dynamical method for zero-range and finite-range
interactions. To apply the dynamical method to finite-range forces, we have
explicitly derived the expression of the energy curvature matrix in momentum
space.
  Finally, the NS crustal properties, moment of inertia and tidal deformability
are thoroughly analyzed using Skyrme and finite-range interactions.
