Since their first allusion, carbon nanotubes have attracted significant research interest, especially with respect to composite manufacturing as a filler material for enhancing their mechanical and electrical properties. Several methods have been developed for modifying the electrical properties of carbon nanotubes such as CNTs wall's carbon atoms substitution with other appropriate atoms including engineering of their outer surfaces by covalent and noncovalent molecules, such as CNTs channel filling and nano-chemical reactions therein. CNTs with tailored electrical conduction open large perspectives for their applicabilities in advanced technologies. Taking into consideration the innovative advantages of pure and hybrid CNTs, in this article we have comprehensively reviewed the latest state-of-art research developments in the direction of different synthesis strategies, structure-property relationships, and advanced applications towards energy storage, supercapacitors, electrodes, catalytic supports, as well as biosensing.