The extraordinary electronic, thermal and mechanical properties of carbon nanotubes (CNTs) closely relate to their structure. They can be seen as rolled-up graphene sheets with their electronic properties depending on how this rolling up is achieved. However, this is not the way they actually grow. Various methods are used to produce carbon nanotubes. They all have in common three ingredients: (i) a carbon source, (ii) catalyst nanoparticles and (iii) an energy input. In the case where the carbon source is provided in solid form, one speaks about 'high temperature methods' because they involve the sublimation of graphite which does not occur below 3200 °C. The first CNTs were synthesized by these techniques. For liquid or gaseous phases, the generic term of 'medium or low temperature methods' is used. CNTs are now commonly produced by these latter techniques at temperatures ranging between 350 and 1000 °C, using metal nanoparticles that catalyze the decomposition of the gaseous carbon precursor and make the growth of nanotubes possible. The aim of this review article is to give a general overview of all these methods and an understanding of the CNT growth process.