The mechanisms by which carbon nanotubes nucleate and grow remain poorly understood. This paper reviews the models which have been proposed to explain nanotube growth in the arc-evaporation and laser-vaporisation processes. Many of the early models assumed that growth is a gas phase phenomenon but there is growing experimental evidence that the formation of both multiwalled and single-walled tubes involves a solid state transformation. Heating rate also seems to be important in promoting nanotube growth. (c) 2006 Elsevier Ltd. All rights reserved.