This review deals with electrospun nanofibers and their applications in several fields. Nanofibers have mainly been produced via electrospinning technique due to the simple, cost-effective, and versatile setup. Electrospinning is defined as a process, which produces fibers from its polymer solutions under exposure of high electric field voltage. The technique needs optimization of several parameters such solution, processing and ambient parameters to refine nanofiber morphology, diameter and porosity. The basic technique has been modified to produce composite fibers and to increase production capacity. Nanofiber characterization methods are summarized with examples. The relation between electrospinning and electrospraying is discussed. Nanofibers have the ability to form highly porous mesh with large surface to volume ratio enhancing its performance for various applications such as water filtration, tissue engineering scaffold, wounds, fiber composites, drug release and protective clothes. Single nanofibers could potentially be used as soft microrobots for drug delivery. Finally, results from modeling and simulations are illustrated.