Tissue engineering plays a vital role in the medical field that addresses the repair, regeneration, and replacement of damaged tissues or organs. The development of drug-eluting electrospun nanofiber composed of biological macromolecules plays a key role in providing localized drug delivery and structural support. This review examines the recent development and impact of electrospun nanofibers in the field of tissue engineering and explores their potential applications. This review also investigates into the fabrication techniques of nanofibers, highlighting the use of biopolymers like collagen and chitosan, chiefly, focuses on understanding the mechanisms of drug-releasing features of these nanofibers. Studies concerning the medical applications of these nanofibers, such as wound healing, skin regeneration, bone tissue engineering, and neural repair, were also reviewed. Beyond the application in tissue regeneration, this review also explores the potential efficacy of nanofibres in cancer therapy, antibacterial activity, enzyme immobilization, and biosensing applications. This study provides an up-to-date critical insight into the applications of electrospun nanofiber application and key scalable production processes, underscoring the potential economic impacts of advanced wound care technologies. While outlining current challenges, this paper also offers future perspectives on the design, application, and potential expansion of drug-eluting electrospun fibers in medical sciences, ultimately showcasing their pivotal role in advancing therapeutic outcomes.