Auxetic materials are known for their unique ability to expand/contract in multiple directions when stretched/compressed. In other words, they exhibit a negative Poisson’s ratio, which is usually positive for most of materials. This behavior appears in some biological tissues such as human skin, where it promotes wound healing by providing an enhanced mechanical support and facilitating cell migration. Skin tissue engineering has been a growing research topic in recent years, largely thanks to the rapid development of 3D printing techniques and technologies. The combination of computational studies with rapid manufacturing and tailored designs presents a huge potential for the future of personalized medicine. Overall, this review article provides a comprehensive overview of the current state of research on auxetic constructs for skin healing applications, highlighting the potential of auxetics as a promising treatment option for skin wounds. The article also identifies gaps in the current knowledge and suggests areas for future research. In particular, we discuss the designs, materials, manufacturing techniques, and also the computational and experimental studies on this topic.