  Heavy-ion reactions induced by neutron-rich nuclei provide a unique means to
investigate the equation of state of isospin-asymmetric nuclear matter,
especially the density dependence of the nuclear symmetry energy. In
particular, recent analyses of the isospin diffusion data in heavy-ion
reactions have already put a stringent constraint on the nuclear symmetry
energy around the nuclear matter saturation density. We review this exciting
result and discuss its implications on nuclear effective interactions and the
neutron skin thickness of heavy nuclei. In addition, we also review the
theoretical progress on probing the high density behaviors of the nuclear
symmetry energy in heavy-ion reactions induced by high energy radioactive
beams.
