Heavy-ion reactions, especially those induced by radioactive beams, provide a unique opportunity to probe the Equation of State (EOS) of neutron-rich nuclear matter in terrestrial nuclear laboratories. The isospin-dependent part of the EOS, i.e., the density dependence of the nuclear symmetry energy, is still rather poorly known especially at supra-saturation densities. However, it is very important for many interesting phenomena in both astrophysics and nuclear physics. In this talk, I shall first discuss why the density dependence of the nuclear symmetry energy is currently very uncertain at supra-saturation densities and what fundamental physics we can learn from studying the symmetry energy. Some recent progress and main challenges of experimentally constraining the high-density symmetry energy will then be discussed. Finally, some astrophysical implications of the currently partially constrained nuclear symmetry energy will be presented.