This review addresses fundamentals and progress in field of thermally conducting polymer/nanocarbon nanocomposite. Upsurge in thermal conductivity of materials may lead to rapid heat diffusion, which in turn may prevent degradation. Thermally conductive nanofillers (carbon nanotube, graphene, nanodiamond, inorganics) have been effectively employed to form desired nanocomposite. In polymer/nanocarbon nanocomposites, thermal conductivity depends on nanofiller type, dispersion, loading level, polymer nature, morphology, and crystallinity. Thermal conductivity parameter has been significantly considered in aerospace, automotive, electronics, and energy-related industries, where thermal dissipation has become a challenging problem. In future, it is desired to design high performance nanocomposites with manageable thermal conduction.