Carbon nanotubes have exceptional mechanical, electrical, and thermal properties, which are strongly anisotropic. In order to fully utilize these properties, numerous carbon nanotube/polymer composite fibers have been produced and investigated. In this review, we summarize recent developments in terms of methods of fiber formation and their resulting properties. Polymer/carbon nanotube fibers can be processed using melt or solution  spinning.  Solutions  spinning  technologies include wet, dry, dry-jet, and gel spinning. Fibers can also be spun using electro spinning. Carbon nanotubes used can be single-wall, double-wall, multi-wall, or vapor grown carbon nano fibers. Most composite fibers processed to date contain less than 10 wt% carbon nanotubes, though there are a few studies where carbon nanotube content is 60 wt% or higher. In most cases, the addition of carbon nanotube results in increased tensile and compressive properties, enhanced fatigue resistance, increased solvent resistance, as well as increased glass transition temperature. Carbon nanotubes act as a template for polymer orientation and a nucleating agent for polymer crystallization. This ability of carbon nanotubes is expected to have profound impact on polymer and fiber processing, as well as on the resulting morphology and properties. The results of studies carried out to date are briefly reviewed in this paper