The continuous improvements in the field of both regenerative medicine and tissue engineering have allowed the design of new and more efficacious strategies for the treatment of chronic or hard-to-heal skin wounds, which represent heavy burden, from a medical and economic point of view. These novel approaches are based on the usage of three key methodologies: stem cells, growth factors, and biomimetic scaffolds. These days, the adipose tissue can be considered the main source of multipotent mesenchymal stem cells, especially adipose-derived stem cells (ASCs). ASCs are easily accessible from various fat depots and show an intrinsic plasticity in giving rise to cell types involved in wound healing and angiogenesis. ASCs can be found in fat grafts, historically used in the treatment of chronic wounds, and have been evaluated as such in both animal models and human trials, to exploit their capability of accelerating wound closure and inducing a correct remodeling of the newly formed fibrovascular tissue. Since survival and fitness of ASCs need to be improved, they are now employed in conjunction with advanced wound dressings, together with dermal regenerative templates and platelet-rich plasma (as a source of growth and healing factors). In this work, we provide an overview of the current knowledge on the topic, based on existing studies and on our own experience.