The challenge on carbon nanotubes is still the subject of many research groups. While in the first years the focus was on the new synthesis methods, new carbon sources and support materials, recently, the application possibilities are the principal arguments of the studies. The three main synthesis methods discussed in this review are the arc discharge, the laser ablation and the chemical vapour deposition (CVD) with a special regard to the latter one. In the early stage of the nanotube production the first two methods were utilized mainly for the production of SWNTs while the third one produced mainly MWNTs. The principle of CVD is the decomposition of various hydrocarbons over transition metal supported catalyst. Single-walled (SWNT), multi-walled (MWNT) and coiled carbon nanotubes are produced. In some case, interesting carbonaceous materials are formed during the synthesis process, such as bamboo-like tubes, onions, horn-like structures. In this paper, we refer to the progresses made in the field of the synthesis techniques of carbon nanotubes in the last decade.