  The nuclear symmetry energy, which describes the energy difference of per
proton and neutron in nuclear matter, has been extensively studied within the
last two decades. Around saturation density, both the value and the slope of
the nuclear symmetry energy have been roughly constrained, its high-density
behavior is now still in argument. Probing high-density symmetry energy at
terrestrial laboratories is being carried out at facilities that offer
radioactive beams worldwide. While relevant experiments are being conducted, we
theoretically developed more advanced isospin-dependent transport model
including new physics such as nucleon-nucleon short-range correlations and
in-medium isospin-dependence of baryon-baryon scattering cross section. New
sensitive probes of high-density symmetry energy are provided, such as
squeezed-out neutron to proton ratio, photon and light cluster as well as the
production of mesons with strangeness or hidden strangeness. The blind spots of
probing the high-density symmetry energy by sensitive observable are
demonstrated. Model dependence of frequently used sensitive probes of the
symmetry energy has been studied thoroughly based on different transport
models. A qualitative observable of neutron to proton ratio at high emitting
energy is proposed to probe the high-density symmetry energy qualitatively. The
probed density regions of the symmetry energy are carefully studied. Effects of
nucleon-nucleon short-range correlations on the some sensitive observables of
the symmetry energy in heavy-ion collisions are explored carefully. Probing the
curvature of the symmetry energy by involving the slope information of the
symmetry energy at saturation point in the transport model is proposed.
