A carbon nanotube fiber is formed by interlocking carbon nanotubes that are perfectly aligned to give a continuous long fiber. The production of neat carbon nanotube fibers has paved the way for realization of superior mechanical and physical properties of individual carbon nanotubes at macroscopic scale. In this review paper, we elucidate the state of the art advances in fabrication methods, characterization, modeling of mechanical properties, and applications of carbon nanotube fibers as next generation high performance fibers for composites. Recommendations have been made on the aspects of design and scale-up for large scale manufacturing of carbon nanotube fibers using (a) a stepwise protocol for the determination rate controlling step(s) and the estimation of overall rate of reaction, and (b) computational fluid dynamics. Finally, the challenges and opportunities in carbon nanotube fiber research have been clearly brought out, and suggestions have been made for future work.