Electrospun nanofiber materials have been considered as advanced dressing candidates in the perspective of wound healing and skin regeneration, originated from their high porosity and permeability to air and moisture, effective barrier performance of external pathogens, and fantastic extracellular matrix (ECM) fibril mimicking property. Gelatin is one of the most important natural biomaterials for the design and construction of electrospun nanofiber-based dressings, due to its excellent biocompatibility and biodegradability, and great exudate-absorbing capacity. Various crosslinking approaches including physical, chemical, and biological methods have been introduced to improve the mechanical stability of electrospun gelatin-based nanofiber mats. Some innovative electrospinning strategies, including blend electrospinning, emulsion electrospinning, and coaxial electrospinning, have been explored to improve the mechanical, physicochemical, and biological properties of gelatin-based nanofiber mats. Moreover, numerous bioactive components and therapeutic agents have been utilized to impart the electrospun gelatin-based nanofiber dressing materials with multiple functions, such as antimicrobial, anti-inflammation, antioxidation, hemostatic, and vascularization, as well as other healing-promoting capacities. Noticeably, electrospun gelatin-based nanofiber mats integrated with specific functions have been fabricated to treat some hard-healing wound types containing burn and diabetic wounds. This work provides a detailed review of electrospun gelatin-based nanofiber dressing materials without or with therapeutic agents for wound healing and skin regeneration applications.