Electrospinning is the simplest and most widely used technology for producing ultra-thin fibers. During electrospinning, the high voltage causes a thin jet to be launched from the liquid polymer and then deposited onto the grounded collector. Depending on the type of the fluid, solution and melt electrospinning are distinguished. The morphology and physicochemical properties of the produced fibers depend on many factors, which can be categorized into three groups: process parameters, material properties, and ambient parameters. In the biomedical field, electrospun nanofibers have a wide variety of applications ranging from medication delivery systems to tissue engineering scaffolds and soft electronics. Many of these showed promising results for potential use as medical devices in the future. Medical devices are used to cure, prevent, or diagnose diseases without the presence of any active pharmaceutical ingredients. The regulation of conventional medical devices is strict and carefully controlled; however, it is not yet properly defined in the case of nanotechnology-made devices. This review is divided into two parts. The first part provides an overview on electrospinning through several examples, while the second part focuses on developments in the field of electrospun medical devices. Additionally, the relevant regulatory framework is summarized at the end of this paper.