The equation of state (EOS) of nuclear matter is one of central issues in nuclear physics. With the establishment or construction of many radioactive beam facilities around the world, such as the Cooling Storage Ring (CSR) facility at HIRFL in Lanzhou, China, the Radioactive Ion Beam (RIB) Factory at RIKEN in Japan, the FAIR/GSI in Germany, SPIRAL2/GANIL in France, and the Facility for Rare Isotope Beams (FRIB) in the United States, it is possible in terrestrial laboratories to explore the EOS of isospin asymmetric nuclear matter under the extreme condition of large isospin asymmetry, especially with regard to the density dependence of the nuclear symmetry energy. This knowledge, especially the latter, is important for understanding not only the structure of radioactive nuclei, the reaction dynamics induced by rare isotopes, and the liquid-gas phase transition in asymmetric nuclear matter, but also many critical issues in astrophysics. In the present talk, we review recent progress in the determination of equation of state for isospin asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy, from heavy-ion collisions. Implications of these results for the nuclear effective interactions, neutron-skin thickness of heavy nuclei and properties of neutron stars are also discussed.

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