Carbon nanotubes (CNTs) are remarkable nanostructures with unique mechanical, electrical, and thermal properties, holding immense potential for various applications in fields such as electronics, materials science, and medicine. This abstract explores the synthesis of carbon nanostructures, particularly focusing on carbon nanotubes, and the development of organometallic fullerene derivatives. The synthesis of carbon nanotubes involves a variety of techniques, including arc discharge, chemical vapor deposition (CVD), and laser ablation, each offering distinct advantages in terms of scalability, purity, and control over structural properties. These methods enable the production of CNTs with tailored characteristics, such as diameter, chirality, and length, to suit specific application requirements. Organometallic fullerene derivatives represent a class of compounds wherein metal atoms or clusters are encapsulated within fullerene cages, offering unique electronic, magnetic, and catalytic properties. The synthesis of these derivatives involves functionalizing fullerene molecules with organometallic precursors through chemical reactions, resulting in hybrid materials with enhanced functionality and versatility. the significance of carbon nanotubes and organometallic fullerene derivatives in advancing nanotechnology and materials science. By understanding their synthesis and properties, researchers can explore novel applications in areas such as nanoelectronics, catalysis, drug delivery, and energy storage, contributing to the development of innovative technologies with societal impact.