Nanotechnology is the study and development of materials at nano levels. It is one of the rapidly growing scientific disciplines due to its enormous potential in creating novel materials that have advanced applications. This technology has tremendously impacted many different science and engineering disciplines, such as electronics, materials science, and polymer engineering. Nanofibers, due to their high surface area and porosity, find applications as filter medium, adsorption layers in protective clothing, etc. Electrospinning has been found to be a viable technique to produce nanofibers. An in-depth review of research activities on the development of nanofibers, fundamental understanding of the electrospinning process, and properties of nanostructured fibrous materials and their applications is provided in this article. A detailed account on the type of fibers that have been electrospun and their characteristics is also elaborated. It is hoped that the overview article will serve as a good reference tool for nanoscience researchers in fibers, textiles, and polymer fields. Furthermore, this article will help with the planning of future research activities and better understanding of nanofiber characteristics and their applications.