Electrospinning is an adaptable and rapidly advancing technique for fabricating fibers and nanofibers characterized by a high surface area-to-volume ratio, which has attracted substantial interest in diverse fields, particularly biomedical engineering. This review examines the principles, construction, and variations of electrospinning techniques, alongside the essential processes, parameters, and challenges related to the development of electrospun nanofibers. The focus is placed on chitosan, a naturally derived polymer known for its distinct properties and biocompatibility, as a candidate material for electrospinning. The general characteristics of chitosan, including its solubility, molecular weight, and degree of deacetylation, are discussed, along with various functional modifications of chitosan derivatives. Additionally, the review explores the biomedical applications of electrospun chitosan nanofibers, particularly in areas such as wound healing, tissue engineering, bone regeneration, nerve regeneration, corneal tissue engineering, intervertebral disc repair, dental tissue engineering, liver tissue engineering, and vascular tissue engineering. The article concludes with an analysis of the current state and future prospects of electrospinning, emphasizing its potential to transform the field of biomedical engineering.