Sensors and biosensors have found applications in many areas, e.g., in medicine and clinical diagnostics, or in environmental monitoring. To expand this field, nanotechnology has been employed in the construction of sensing platforms. Because of their properties, such as high surface area to volume ratio, nanofibers (NFs) have been studied and used to develop sensors with higher loading capacity, better sensitivity, and faster response time. They also allow to miniaturize designed platforms. One of the most commonly used techniques of the fabrication of NFs is electrospinning. Electrospun NFs can be used in different types of sensors and biosensors. This review presents recent studies concerning electrospun nanofiber-based electrochemical and optical sensing platforms for the detection of various medically and environmentally relevant compounds, including glucose, drugs, microorganisms, and toxic metal ions.