This work examines the recent developments in non-traditional catalyst-assisted chemical vapour deposition of carbon nanotubes (CNTs) with a view to determining the essential role of the catalyst in nanotube growth. A brief overview of the techniques reliant on the structural reorganization of carbon to form CNTs is provided. Additionally, CNT synthesis methods based upon ceramic, noble metal, and semiconducting nanoparticle catalysts are presented. Experimental evidence is provided for CNT growth using noble metal and semiconducting nanoparticle catalysts. A model for CNT growth consistent with the experimental results is proposed, in which the structural reorganization of carbon to form CNTs is paramount.