Electrospinning is a method of preparing microfibers or nanofibers by using an electrostatic force to stretch the electrospinning fluid. Electrospinning has gained considerable attention in many fields due to its ability to produce continuous fibers from a variety of polymers and composites in a simple way. Electrospun nanofibers have many merits such as diverse chemical composition, easily adjustable structure, adjustable diameter, high surface area, high porosity, and good pore connectivity, which give them broad application prospects in the biomedical field. This review systematically introduced the factors influencing electrospinning, the types of electrospun fibers, the types of electrospinning, and the detailed applications of electrospun fibers in controlled drug release, biological dressings, tissue repair and enzyme immobilization fields. The latest progress of using electrospun fibers in these fields was summarized, and the main challenges to be solved in electrospinning technology were put forward.