Polymer fibers with diameters in the micrometer range have been extensively used in a large variety of applications ranging from textile fabrics to fiber-reinforced materials. With the rapid development in nanoscience and nanotechnology, there is an ever increasing demand for polymer fibers with diameters down to the nanometer scale. Conducting polymer nanofibers are of particular interest for various applications, ranging from chem-/bio-sensors to electronic devices. Electrospinning has been used to produce nanofibers from various polymers. In particular, electrospun nanofibers based on polymer/carbon nanotube (CNT) composites are also very attractive multifunctional nanomaterials for many potential applications; the confinement-enhanced CNT alignment within such nanofibers have been shown to greatly improve the fiber mechanical and electrical properties. In this article, we summarize recent research progress on electrospun polymers and polymer/CNT composite nanofibers, with an emphasis on those based on conducting polymers and CNTs for potential applications.