Bulk polymers are often regarded as thermal insulators due to low thermal conductivity, which extremely limits their applications in the field of heat transfer. Over the past decades, thermal transport in polymers, and polymer nanocomposites has been intensively studied on both theoretical and experimental levels. In addition, novel thermal transport phenomenon involving divergent thermal conductivity in individual polymer chains, giant thermal rectification, has been observed. In this review, the mechanism behind thermal transport in materials, interfacial thermal transport, thermal rectification in polymers, and enhancing thermal transport of polymers are firstly addressed. Secondly, the computational methods for investigating the thermal property of materials mainly focused on molecular dynamics (MD) simulation are summarized and compared. The advanced spectral decomposition methods in non-equilibrium molecular dynamics (NEMD) simulation are highlighted. Thirdly, experimental advances relevant to thermal transport of polymers are briefly reviewed. Finally, the challenges and outlook about modulating thermal transport in polymers and polymer nanocomposites are pinpointed.