  The structure and composition of the inner crust of neutron stars, as well as
global stellar properties such as radius and moment of inertia, have been shown
to correlate with parameters characterizing the symmetry energy of nuclear
matter such as its magnitude J and density dependence L at saturation density.
It is thus mutually beneficial to nuclear physicists and astrophysicists to
examine the combined effects of such correlations on potential neutron star
observables in the light of recent experimental and theoretical constraints on
J, L, and relationships between them. We review some basic correlations between
these nuclear and astrophysical observables, and illustrate the impact of
recent progress in constraining the J-L parameter space on the composition of
the inner crust, crust-core transition density and pressure, and extent of the
hypothesized pasta region. We use a simple compressible liquid drop model in
conjunction with a simple model of nuclear matter which allows for independent,
smooth, variation of the J and L. We extend the model into the core using the
same nuclear matter model to explore the effects on global crust and core
properties, and on potential observables such as crust oscillation frequencies
and mechanically supported crust deformation. Throughout we illustrate the
importance of the relationship between J and L implicit in a particular model
of nuclear matter to the predictions of neutron star properties.
