The timely management of skin wounds has been an unmet clinical need for centuries. While there have been several attempts to accelerate wound healing and reduce the cost of hospitalisation and the healthcare burden, there remains a lack of efficient and effective wound healing approaches. In this regard, stem cell-based therapies have garnered an outstanding position for the treatment of both acute and chronic skin wounds. Stem cells of different origins (e.g., embryo-derived stem cells) have been utilised for managing cutaneous lesions; specifically, mesenchymal stem cells (MSCs) isolated from foetal (umbilical cord) and adult (bone marrow) tissues paved the way to more satisfactory outcomes. Since angiogenesis plays a critical role in all four stages of normal wound healing, recent therapeutic approaches have focused on utilising stem cells for inducing neovascularisation. In fact, stem cells can promote angiogenesis via either differentiation into endothelial lineages or secreting pro-angiogenic exosomes. Furthermore, particular conditions (e.g., hypoxic environments) can be applied in order to boost the pro-angiogenic capability of stem cells before transplantation. For tissue engineering and regenerative medicine applications, stem cells can be combined with specific types of pro-angiogenic biocompatible materials (e.g., bioactive glasses) to enhance the neovascularisation process and subsequently accelerate wound healing. As such, this review article summarises such efforts emphasising the bright future that is conceivable when using pro-angiogenic stem cells for treating acute and chronic skin wounds.