Wound dressings have experienced continuous and significant changes since the ancient times. The development starts with the use of natural materials to simply cover the wounds to the materials of the present time that could be specially made to exhibit various extraordinary functions. The modern bandage materials made of electrospun biopolymers contain various active compounds that are beneficial to the healing of wounds. These materials are fibrous in nature, with the size of fibers segments ranging from tens of nanometers to micrometers. With the right choices of biopolymers used for these fibrous materials, they could enhance the healing of wounds significantly compared with the conventional fibrous dressing materials, such as gauze. These bandages could be made such that they contain bioactive ingredients, such as antimicrobial, antibacterial, and antiinflammatory agents, which could be released to the wounds enhancing their healing. In an active wound dressing (AWD), the main purpose is to control the biochemical states of a wound in order to aid its healing process. This review provides an overview of different types of wounds, effective parameters in wound healing and different types of wound dressing materials with a special emphasis paid to those prepared by electrospinning.