Wound healing is a dynamic series of interconnected events with the ultimate goal of promoting neotissue formation and restoration of anatomical function. Yet, the complexity of wound healing can often result in development of complex, chronic wounds, which currently results in a significant strain and burden to our healthcare system. The advancement of new and effective wound care therapies remains a critical issue, with the current therapeutic modalities often remaining inadequate. Notably, the field of tissue engineering has grown significantly in the last several years, in part, due to the diverse properties and applications of polymeric biomaterials. The interdisciplinary cohesion of the chemical, biological, physical, and material sciences is pertinent to advancing our current understanding of biomaterials and generating new wound care modalities. However, there is still room for closing the gap between the clinical and material science realms in order to more effectively develop novel wound care therapies that aid in the treatment of complex wounds. Thus, in this review, we discuss key material science principles in the context of polymeric biomaterials, provide a clinical breadth to discuss how these properties affect wound dressing design, and the role of polymeric biomaterials in the innovation and design of the next generation of wound dressings.