SiC ceramics have important applications in energy conservation, semiconductor, and nuclear industries due to their outstanding resistance to high temperature, corrosion and irradiation, coupled with exceptional intrinsic thermal conductivity. Nevertheless, the thermal conductivity of SiC ceramics at room temperature typically ranges from 30 to 270 W/mK, which is substantially lower than the intrinsic value of 490 W/mK observed in SiC single crystals. This reduction in thermal conductivity has been attributed to factors including impurities within the SiC lattice, grain boundaries, residual secondary phases, and pores. This paper aims to review the influence of microstructural factors such as lattice defects, grain size, alpha/(3 phase composition, grain boundary phase, and porosity on the thermal conductivity of SiC ceramics while revealing the underlying mechanisms. It has been proved that decreased lattice oxygen content, completion of (3-*alpha phase transformation, enlarged grain size, cleaner grain boundaries and highly crystallized grain boundary phase are beneficial for improving thermal conductivity of SiC ceramic. Furthermore, this study analyzes various methods for tailoring these microstructures and provides recommendations for fabricating SiC ceramics with high thermal conductivity. It is proposed that utilizing (3-SiC starting powder with high purity and low oxygen content, using aluminum-free additives capable of efficiently eliminating lattice oxygen and facilitating grain growth, ensuring sufficiently high sintering temperature and extending holding time are effective in obtaining high thermal conductive SiC ceramics.