Neutron stars are highly condensed stellar objects produced in supernova explosions, the end point in the evolution of more massive stars. The masses of neutron stars are approximately in the range of 1-2 times of the sun, whereas their typical radii are only 10-20km. The matter they contain, primarily neutrons, is therefore the densest found outside black holes in the universe. Neutron stars thus provide a laboratory to test our understanding of nature at the extreme, and verify our theories of matter, energy and their interactions. However, neutron stars are still among the most mysterious objects in the universe and they pose a great scientific challenge. The structure and properties of neutron stars are determined by the Equation of State (EOS which is a relationship among pressure, density and temperature) of neutron-rich nuclear matter. For the latter, what has been most uncertain is the density dependence of nuclear symmetry energy related to the energy cost of converting protons into neutrons in nuclear medium at various densities.  Nuclear reactions conducted in terrestrial laboratories, especially heavy-ion reactions induced by highly neutron-rich radioactive beams, can produce nuclear matter similar to those contained in neutron stars. In this talk, I will first review the latest progress in constraining the EOS of neutron-rich nuclear matter especially the density dependence of nuclear symmetry energy around and below the saturation density of nuclear matter. I will then discuss a few open questions regarding the symmetry energy at supra-saturation densities. Finally, several ramifications of nuclear symmetry energy on properties of neutron stars and gravitational waves will be discussed.