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One of the major tasks of studying isospin physics via heavy-ion reactions with neutron-rich nuclei, is to explore the isospin dependence of in-medium nuclear effective interactions and the equation of state of neutron-rich nuclear matter, i.e., the density dependence of nuclear symmetry energy.Because of its great importance for understanding many phenomena in both nuclear physics and astrophysics, the study of the density dependence of nuclear symmetry energy has been the main focus of the intermediate-energy heavy-ion physics community during the last decade.Nowadays significant progress has been achieved in studying the low density behavior of nuclear symmetry energy, but the high density behavior of nuclear symmetry energy is still very uncertain.Theoretically, a number of observables have been proposed as sensitive probes to the high density behavior of nuclear symmetry energy.With new opportunities provided by the various radioactive beam facilities being constructed around the world, studies of the high density behavior of nuclear symmetry energy is expected to be one of the main forefront research areas in nuclear physics in the near future.In this contribution, based on the transport model IBUU we review the major progress achieved in studying the high density behavior of nuclear symmetry energy and discuss future challenges in this field.