Since their first discovery, carbon nanotubes (CNTs) have become a material central to the field of nanotechnology. Owing to their splendid physical, structural and chemical properties, they have the potential to impact a wide range of applications, including advanced ceramics, nanoelectronic devices, nanoscale sensors, solar cells, battery electrodes, and field emitters. This review summarizes the synthetic methods of preparing CNTs and focuses on the chemical vapor deposition (CVD) method, especially catalytic CVD. In order to stabilize and disperse the catalyst nanoparticles (NPs) during synthesis, zeolite was implemented as the template to support metal-containing NPs, so that both CNTs in the bulk and on a 2D substrate were successfully synthesized. Despite more challenges ahead, there is always hope for widespread ever-new applications for CNTs with the development of technology.