  We present various properties of nuclear and compact-star matter, comparing
the predictions from two kinds of phenomenological approaches: relativistic
models (both with constant and density-dependent couplings) and
non-relativistic Skyrme-type interactions. We mainly focus on the liquid-gas
instabilities that occur at sub-saturation densities, leading to the
decomposition of the homogeneous matter into a clusterized phase. Such study is
related to the description of neutron-star crust (at zero temperature) and of
supernova dynamics (at finite temperature).
