  Determining the Equation of State (EOS) of dense neutron-rich nuclear matter
is a shared goal of both nuclear physics and astrophysics. Except possible
phase transitions, the density dependence of nuclear symmetry \esym is the most
uncertain part of the EOS of neutron-rich nucleonic matter especially at
supra-saturation densities. Much progresses have been made in recent years in
predicting the symmetry energy and understanding why it is still very uncertain
using various microscopic nuclear many-body theories and phenomenological
models. Simultaneously, significant progresses have also been made in probing
the symmetry energy in both terrestrial nuclear laboratories and astrophysical
observatories. In light of the GW170817 event as well as ongoing or planned
nuclear experiments and astrophysical observations probing the EOS of dense
neutron-rich matter, we review recent progresses and identify new challenges to
the best knowledge we have on several selected topics critical for
understanding astrophysical effects of the nuclear symmetry energy.
