Electrospinning has been recognized as an efficient technique for the fabrication of polymer nanofibers. Various polymers have been successfully electrospun into ultrafine fibers in recent years mostly in solvent solution and some in melt form. Potential applications based on such fibers specifically their use as reinforcement in nanocomposite development have been realized. In this paper, a comprehensive review is presented on the researches and developments related to electrospun polymer nanofibers including processing, structure and property characterization, applications, and modeling and simulations. Information of those polymers together with their processing conditions for electrospinning of ultrafine fibers has been summarized in the paper. Other issues regarding the technology limitations, research challenges, and future trends are also discussed.