Polymer nanofibers, with diameters in the nanometer range, possess larger surface areas per unit mass and permit easier addition of surface functionalities compared with polymer microfibers. Hence, polymer nanofiber mats are being considered for use as filters, scaffolds for tissue engineering, protective clothing, reinforcement in composite materials and sensors. Although some of these applications are in the development stage, a few have been commercially exploited. Research on polymer nanofibers, nanofiber mats, and their applications has seen a remarkable growth over the last few years. However, a review of the various issues related to these nanofibers has not been published. This article presents a review of the recent trends in the processing methods and characterization techniques for polymer nanofibers. Research challenges and future trends in the processing and characterization of polymer nanofibers are discussed in the article. Five processing methods have been examined in this review, namely drawing, template synthesis, phase separation, self-assembly, and electrospinning. Among these methods, electrospinning has been used to convert a large variety of polymers into nanofibers and may be the only process that has the potential for mass production. The structure, morphology, and geometry of nanofibers and the porosity and tensile properties of nanofiber mats can be investigated through conventional techniques and instruments. But new techniques are needed for the mechanical testing of single nanofibers. Although measurement of mechanical properties such as tensile modulus, strength, and elongation is difficult because of the small diameters of the fibers, these properties are crucial for the proper use of nanofiber mats.