Chronic wounds present a multifactorial clinical challenge characterized by prolonged inflammation, microbial biofilm formation, oxidative stress, and impaired vascularization. Conventional wound dressings such as films, hydrogels, and decellularized matrices often fall short due to limited bioactivity, inadequate mechanical properties, and insufficient control over therapeutic delivery. This review highlights electrospun nanofiber membranes as advanced biomimetic platforms that replicate the structural and functional attributes of the extracellular matrix while enabling localized and sustained release of therapeutic agents. The novelty of this work lies in its systematic association of bioactive compounds including antimicrobial, antioxidant, immunomodulatory, oxygen releasing, and hemostatic agents with their specific biological targets in chronic wound healing. Also, the review critically examines fabrication techniques such as coaxial, emulsion, gas assisted, and stimuli responsive electrospinning, and evaluates how key processing parameters influence fiber morphology, drug release profiles, and cellular interactions. By integrating material science with mechanistic insight, this work provides a unified framework for the rational design of responsive nanofiber based wound dressings and outlines future directions involving smart delivery systems, biosensing integration, and three dimensional bioprinting to support clinical translation and personalized therapy. Emphasis is also placed on emerging multifunctional membranes capable of real-time interaction with wound pathophysiology. Challenges related to scalability, regulatory approval, and long-term biocompatibility are discussed to bridge the gap between laboratory findings and clinical adoption. This review ultimately serves as a foundation for developing next generation wound care strategies that are both mechanistically targeted and clinically adaptable.