Electrospinning, a remarkable and versatile technique has been related to medical textiles, aiming to produce nanomaterials for drug delivery and tissue regeneration applications. Furthermore, electrospun nanofibrous materials with unique properties as favorable pore size distribution, porosity, surface area, and wettability, along with effective mechanical properties, are the frontrunner solutions. Also, the features of the nanofibrous structures can be designed and optimized by controlling electrospinning parameters related to the solution properties, the setup parameters, and the environmental conditions to design nanofibrous textile materials for the desired applications. Further, to accomplish the required functionality of the drug-delivery systems, a rather broad range of drugs have been loaded into the nanofibers using different electrospinning techniques, namely the blending, side-by-side, coaxial, tri-axial, emulsion, and multi-needle electrospinning, in order to accomplish specific drug-release profiles of the designed nanofibrous textiles. Thus, this chapter describes the different electrospinning techniques that have been utilized in the production of the textile nanofibrous materials as the application of these materials in bone, nerve, periodontal, and vascular regeneration, as well as in wound dressings, personal-protective-equipment (PPE), and cancer treatment, providing an overview of the recent studies and highlighting the current challenges and future perspectives for their medical applications.