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Thermal management systems, controlling the dispersion, storage and conversion of heat, were widely used in various fields of national economy and defence applications <i>etc</i>. Advanced thermal management materials form the material basis of the thermal management system, while the thermal conductivity was the critical property of all the thermal management materials. The application, classification, and physical mechanism of heat conduction of advanced thermal management materials were reviewed in this paper. The research progress and existing problems of thermal interface materials, high thermal conductivity packaging materials, thermal storage materials and thermoelectric materials were introduced. It is pointed out that molecular dynamics, density functional theory and large-scale parallel computing technology will play increasingly import roles in revealing the multi-scale heat transfer mechanism in the homogeneous and composite materials.