Carbon nanotubes (CNTs) are potential candidates for heat removal materials that dissipate heat from devices because of their high thermal conductivity, mechanical stiffness and flexibility. The fact that the thermal management is one of the key issues for next generation electronics has attracted much attention to the thermal transport properties of CNT. Computational simulations have served as powerful tools not only to predict the CNT thermal transport properties but also to gain insight into detailed and unique characteristics that are not yet accessible in experiments. In this paper, we present an overview of recent progress on theoretical and computational research on thermal transport in CNTs and see how they compare with recent experimental results.