Carbon nanotubes have been the focus of considerable research since their observation from 1991 onwards. The extensive basic studies performed by physicists and chemists in the processing of carbon nanotubes during the past decade have established a sound foundation for exploring their technological application. The exceptional mechanical properties of carbon nanotubes can be exploited in the development of nanotube-based composite materials that may far exceed the properties of existing fiber-reinforced composites. Nanocomposites of carbon tubes that have extraordinary specific stiffness and specific strength represent a tremendous opportunity for application in the 21st century. This paper provides a concise review of the recent advancement in carbon nanotubes and their composites. We examine the research work reported in the literature on the structure and processing of carbon nanotubes, as well as the characterization and modeling of the properties of carbon nanotubes and their composites.