Carbon nanostructures such as nanotubes, nanofibers and graphene have gained great attention over the past two decades. Owing to their unique properties, these nanomaterials have been proposed for use in a wide range of applications. For example, carbon nanostructures typically exhibit high thermal conductivities, making them particularly attractive for thermal management of electronics. Accurate and efficient thermal characterization holds the key to understanding the thermal transport mechanisms in these materials to assure their continued development for novel applications. This presentation will describe the techniques used for the characterization of thermal transport in individual carbon nanostructures and nanocomposites such as the thermal flash technique, developed in our laboratory. The thermal conductivities measured for vapor-grown carbon nanofibers and various graphene nanoplatelets will also be presented and discussed. The results provide great insight to how properties such as oxygen content and size influence the inherent thermal conductivity of these nanostructures. This presentation will also describe studies on epoxy-graphite-graphene nanocomposites and present results of an unusually high thermal conductivity, greater than 40 W/m-K, which is a nearly 250 times enhancement compared to the native matrix material. As will be discussed, the unexpectedly high thermal conductivity can be attributed to a synergistic effect that arises due to the presence of both the graphite and graphene fillers.