Abstract: 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-dependent baryon-baryon scattering cross section. New sensitive probes of the 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 dependences of frequently used sensitive probes of the symmetry energy have been studied thoroughly based on different transport models. A qualitative observable of neutron to proton ratio at high kinetic energy is proposed to probe the high-density symmetry energy qualitatively. The probed density regions of the symmetry energy by some observables are first studied and usually lower probed density regions comparing with maximum compression density are obtained. Nucleon-nucleon short-range correlations usually reduce values of sensitive observables of the symmetry energy. 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. Besides constraining the high-density symmetry energy by using heavy-ion collisions, a lot of neutron-star related observations from heaven may also be used to constrain the high-density symmetry energy.