Abstract: Numerical heat transfer of liquid lead-bismuth eutectic (LBE) is limited by the extremely low-Prandtl-number characteristic, conventional Reynolds analogy method fails to accurately close and describe the turbulent heat flux (THF) in the averaged energy equation and the temperature transport process. Therefore, it is necessary to construct models specifically for the closure of THF in low-Prandtl-number fluids. The models are divided into four categories: turbulent-Prandtl-number models, algebraic heat flux models, second-moment differential heat flux models, and data-driven models using machine learning. This study provides insights into subsequent research, optimization, and innovation in THF closure modeling by reviewing their research progress, modeling concepts, the complexity demonstrated by the models, and their applicability in engineering applications. In the simulation of forced convection heat transfer between fuel rod bundles in LBE, explicit algebraic heat flux models show promising application prospects, while machine learning provides a fresh perspective for THF closure.