In recent years, spinning techniques have been highlighted for their capability of producing complex, fibrous and reticulated constructs with great potential for biomedicine. Indeed, biodegradable constructs based on polymeric fibers are desirable in wound healing due to their large surface area, interconnectivity, open pore structure, and controlled mechanical strength. Modern dressings made of spun biopolymers can incorporate active compounds within their matrix, which can be delivered topically, very beneficial to the healing process. In the present work, we explore the spinning techniques used to process polymers in the form of fibers, assess the properties of some of the most common biodegradable polymers used in wound dressing production, and highlight the potentialities of important biomolecules used in the production of new generation of bioactive wound dressings.