Drug-eluting medical textiles have recently gained great attention to be used in different applications due to their cost effectiveness and unique physical and chemical properties. Using various fiber production and textile fabrication technologies, fibrous constructs with the required properties for the target drug delivery systems can be designed and fabricated. This review summarizes the current advances in the fabrication of drug-eluting medical textiles. Different fiber production methods such as melt-, wet-, and electro-spinning, and textile fabrication techniques such as knitting and weaving are explained. Moreover, various loading processes of bioactive agents to obtain drug-loaded fibrous structures with required physicochemical and morphological properties, drug delivery mechanisms, and drug release kinetics are discussed. Finally, the current applications of drug-eluting fibrous systems in wound care, tissue engineering, and transdermal drug delivery are highlighted.