To pin down the Equation of State (EOS) of dense neutron-rich nucleonic matter has long been a major science driver for both nuclear physics and astrophysics. Nuclear symmetry energy encoding the energy cost of converting protons into neutrons in nuclear medium has been the most uncertain part of the EOS of dense matter in neutron stars. The magnitude and density dependence of nuclear symmetry energy affect the radii, tidal polarization and cooling rates of neutron stars as well as the strain amplitude and frequencies of gravitational waves from both spiraling neutron star binaries and oscillations of isolated neutron stars. Nuclear reactions especially those induced by highly neutron-rich radioactive beams, provide a unique means to probe experimentally the symmetry energy of neutron-rich matter in terrestrial laboratories. In this talk, we will discuss several outstanding issues concerning the EOS of dense neutron-rich matter, its astrophysical impacts and current efforts to constrain the EOS by combining terrestrial nuclear reaction experiments as well as observations of neutron stars using X-rays and gravitational waves.
