  The ultimate goal of studying isospin physics via heavy-ion reactions with
neutron-rich, stable and/or radioactive nuclei is to explore the isospin
dependence of in-medium nuclear effective interactions and the equation of
state of neutron-rich nuclear matter, particularly the isospin-dependent term
in the equation of state, i.e., the density dependence of the symmetry energy.
Because of its great importance for understanding many phenomena in both
nuclear physics and astrophysics, the study of the density dependence of the
nuclear symmetry energy has been the main focus of the intermediate-energy
heavy-ion physics community during the last decade, and significant progress
has been achieved both experimentally and theoretically. In particular, a
number of phenomena or observables have been identified as sensitive probes to
the density dependence of the nuclear symmetry energy. Experimental studies
have confirmed some of these interesting isospin-dependent effects and allowed
us to constrain relatively stringently the symmetry energy at sub-saturation
densities. The impacts of this constrained density dependence of the symmetry
energy on the properties of neutron stars have also been studied, and they were
found to be very useful for the astrophysical community. With new opportunities
provided by the various radioactive beam facilities being constructed around
the world, the study of isospin physics is expected to remain one of the
forefront research areas in nuclear physics. In this report, we review the
major progress achieved during the last decade in isospin physics with heavy
ion reactions and discuss future challenges to the most important issues in
this field.
