The diversity of thermal transport properties in carbon nanomaterials enables them to be used in different thermal fields such as heat dissipation, thermal management, and thermoelectric conversion. In the past two decades, much effort has been devoted to study the thermal conductivities of different carbon nanomaterials. In this review, different theoretical methods and experimental techniques for investigating thermal transport in nanosystems are first summarized. Then, the thermal transport properties of various pure carbon nanomaterials including 1D carbon nanotubes, 2D graphene, 3D carbon...