  Properties of asymmetric nuclear matter are derived from various many-body
approaches. This includes phenomenological ones like the Skyrme Hartree-Fock
and relativistic mean field approaches, which are adjusted to fit properties of
nuclei, as well as more microscopic attempts like the Brueckner-Hartree-Fock
approximation, a self-consistent Greens function method and the so-called
$V_{lowk}$ approach, which are based on realistic nucleon-nucleon interactions
which reproduce the nucleon-nucleon phase shifts. These microscopic approaches
are supplemented by a density-dependent contact interaction to achieve the
empirical saturation property of symmetric nuclear matter. The predictions of
all these approaches are discussed for nuclear matter at high densities in
$\beta$-equilibrium. Special attention is paid to behavior of the isovector
component of the effective mass in neutron-rich matter.
