Wound dressings play an important role in a patient's recovery from health problems, as unattended wounds could lead to serious complications such as infections or, ultimately, even death. Therefore, wound dressings since ancient times have been continuously developed, starting from simple dressings from natural materials for covering wounds to modern dressings with functionalized materials to aid in the wound healing process and enhance tissue repair. However, understanding the nature of a wound and the subsequent healing process is vital information upon which dressings can be tailored to ensure a patient's recovery. To date, much progress has been made through the use of nanomedicine in wound healing due to the ability of such materials to mimic the natural dimensions of tissue. This review provides an overview of recent studies on the physiology of wound healing and various wound dressing materials made of nanofibers fabricated using the electrospinning technique.