In recent years, the understanding and accurate simulation of carbon nanotube-based transistors has become very challenging. Conventional simulation tools of microelectronics are necessary to predict the performance and use of nanotube transistors and circuits, but the models need to be refined to properly describe the full complexity of such novel type of devices at the nanoscale. Indeed, many issues such as contact resistance, low dimensional electrostatics and screening effects, demand for more accurate quantum approaches. This article reviews recent progresses on multiscale simulations which aim at bridging first principles calculations with compact modelling, including the comparison between semi-classical Monte Carlo and quantum transport approaches. (C) 2013 Elsevier Ltd. All rights reserved.