Wound healing is a complex and intriguing phenomenon, in which various biological cells and biomolecules interplay in the injured site. A variety of therapeutics has been used to improve the healing process of wounds. Similarly, various advanced biomaterials have so far been used to deliver stem cells for wound healing. Given that stem cells are the core entities of cell therapy of wounds, they need to be safely delivered by biocompatible scaffolds made using bioactive materials. Such a transformative approach demands multi/transdisciplinary knowledge and technologies essential for wound healing and skin regeneration. Notably, novel wound healing modalities, ranging from bio-inspired materials to cell-derived matrices, have made a paradigm shift in this field. Different types of stem cells such as umbilical cord-, bone marrow-, muscle-, adipose-, and placenta-derived stem cells have been successfully implemented to heal a variety of wounds, using biomaterials like poly(glycolic acid), poly(lactic acid), poly(lactic-co-glycolic acid), collagen, chitosan, gelatin, polycaprolactone, hyaluronic acid, and silicone. In this review, we elaborate on the recent advancements of biopolymers' applications in wound healing and skin regeneration.