Nanofibrous membranes have gained interest for their small pore size, light weight, and excellent filtration. When produced from high-performance polymers, nanofibrous membranes also benefit from excellent mechanical properties, thermal resistance, and chemical resistance. Electrospinning is a common method of producing high-performance nanofibres. However, there are still major challenges with the dissolution and electrospinning of these polymers, as well as in the performance of the resulting nanofibres, which is often less than what would be expected from a conventional high-performance fibre. This review assesses the state of progress in the electrospinning of five high-performance fibres: meta-aramid (m-aramid), para-aramid (p-aramid), polyamide-imide (PAI), polybenzoxazole (PBO), and polybenzimidazole (PBI). Polymers that can be readily dissolved in organic solvents, such as m-aramid, PAI, and PBI, have been more widely researched for electrospinning compared to those that can only be spun from precursors or dissolved in non-volatile solvents. Major focuses within the literature include optimizing the electrospinning process and improving the mechanical performance of the nanofibres. This review demonstrates a clear need for more standardized characterization methods and consideration for the longevity of the nanofibrous membranes. Future research should also focus on scale-up methods of electrospinning so that the benefits of nanofibres made from high-performance polymers can be leveraged by the industry.