Electrospinning is a promising method for the rapid and cost-effective production of nanofibers from a wide variety of polymers given the high surface area morphology of these nanofibers, they make excellent wound dressings, and so have significant potential in the prevention and treatment of scars. Wound healing and the resulting scar formation are exceptionally well-characterized on a molecular and cellular level. Despite this, novel effective anti-scarring treatments which exploit this knowledge are still clinically absent. As the process of electrospinning can produce fibers from a variety of polymers, the treatment avenues for scars are vast, with therapeutic potential in choice of polymers, drug incorporation, and cell-seeded scaffolds. It is essential to show the new advances in this field; thus, this review will investigate the molecular processes of wound healing and scar tissue formation, the process of electrospinning, and examine how electrospun biomaterials can be utilized and adapted to wound repair in the hope of reducing scar tissue formation and conferring an enhanced tensile strength of the skin. Future directions of the research will explore potential novel electrospun treatments, such as gene therapies, as targets for enhanced tissue repair applications. With this class of biomaterial gaining such momentum and having such promise, it is necessary to refine our understanding of its process to be able to combine this technology with cutting-edge therapies to relieve the burden scars place on world healthcare systems.