Chronic wounds occur as a consequence of a prolonged inflammatory phase during the healing process, which precludes skin regeneration. Typical treatment for chronic wounds includes application of autografts, allografts collected from cadaver, and topical delivery of antioxidant, anti-inflammatory, and antibacterial agents. Nevertheless, the mentioned therapies are not sufficient for extensive or deep wounds. Moreover, application of allogeneic skin grafts carries high risk of rejection and treatment failure. Advanced therapies for chronic wounds involve application of bioengineered artificial skin substitutes to overcome graft rejection as well as topical delivery of mesenchymal stem cells to reduce inflammation and accelerate the healing process. This review focuses on the concept of skin tissue engineering, which is a modern approach to chronic wound treatment. The aim of the article is to summarize common therapies for chronic wounds and recent achievements in the development of bioengineered artificial skin constructs, including analysis of biomaterials and cells widely used for skin graft production. This review also presents attempts to reconstruct nerves, pigmentation, and skin appendages (hair follicles, sweat glands) using artificial skin grafts as well as recent trends in the engineering of biomaterials, aiming to produce nanocomposite skin substitutes (nanofilled polymer composites) with controlled antibacterial activity. Finally, the article describes the composition, advantages, and limitations of both newly developed and commercially available bioengineered skin substitutes.