A fuel cell is an electrochemical device that converts the chemical energy of a fuel and oxidant into electricity. Cation-exchange and anion-exchange membranes play an important role in hydrogen fed proton-exchange membrane (PEM) and anion-exchange membrane (AEM) fuel cells, respectively. Over the past 10 years, there has been growing interest in using nanofiber electrospinning to fabricate fuel cell PEMs and AEMs with improved properties, e.g., a high ion conductivity with low in-plane water swelling and good mechanical strength under wet and dry conditions. Electrospinning is used to create either reinforcing scaffolds that can be pore-filled with an ionomer or precursor mats of interwoven ionomer and reinforcing polymers, which after suitable processing (densification) form a functional membrane. In this review paper, methods of nanofiber composite PEMs and AEMs fabrication are reviewed and the properties of these membranes are discussed and contrasted with the properties of fuel cell membranes prepared using conventional methods. The information and discussions contained herein are intended to provide inspiration for the design of high-performance next-generation fuel cell ion-exchange membranes.