Superconducting nanofibers have attracted much attention in basic researches and practical applications due to their unique physical properties such as broad phase transition temperature, excellent heat conductivity, and high critical current density, etc. Electrospinning, as a common method to prepare nanofibers, also has many applications for the preparation of superconducting nanofibers. However, a few of the new methods to fabricate superconducting nanofibers via electrospinning still need further investigations. This review firstly introduces several potential electrospinning methods to obtain superconducting nanofibers, then proceeds to summarize the recent progress in the field of electrospun superconducting materials. The preparation process, difficulties and problems, physical properties of the superconducting nanofibers or nanonetworks (such as superconducting transition temperature, critical current density, critical magnetic field strength, fiber morphology, and structure, etc), theoretical analysis of the properties, and the techniques to improve the performance are also reviewed. In addition, some suggestions and prospects for the development and applications of electrospun superconducting materials in the future are discussed.