Electrospinning is a very powerful technique to produce highly complex nanofibers with tunable properties. This technique provides efficiency, versatility, and low cost to create nanofiber assemblies from a rich variety of natural and synthetic polymers combined with different types of nanoparticles. Electrospun nanofiber materials have demonstrated significant potential in various applications, such as sensors and biosensors, tissue engineering, drug delivery, energy conversion, and storage. This is mainly due to their unique characteristics including mechanical strength, large specific surface area, diverse polymer composition, and simple manufacturing process. Nanofiber-based biosensors offer several advantages over conventional biosensors, including enhanced responsiveness, wider linear range, higher sensitivity, lower limit of detection (LOD), and cost-effectiveness. Recently, there has been considerable interest in developing nanobiocomposites by integrating bioreceptors and conductive nanomaterials into carbon, metal oxide, or polymer electrospun nanofibers. In this comprehensive review, we explore advanced biosensors based on electrospinning technology, including biosensors modified with electrospun carbon, metal/metal oxide, as well as polymer-based and polymer-modified biosensors. After a general and short description of the electrospinning process and electrospinning conditions affecting the production of different nanofibers, the application of electrospun nanofibers for the design of electrochemical (bio)sensors is discussed.