Human skin is particularly vulnerable to external damaging influences such as irradiation, extreme temperatures, chemical trauma, and certain systemic diseases, which reduce the skin's capacity for regeneration and restoration and can possibly lead to large-scale skin defects. To restore skin continuity in severe cases, surgical interventions such as the transplantation of autologous tissue are needed. Nevertheless, the coverage of larger skin defects caused by severe third-grade burns or extensive irradiation therapy is limited due to the depletion of uninjured autologous tissue. In such cases, many of the patient's epidermal cells can become available using biofabricated skin grafts, thereby restoring the skin's vital functions. Given the limited availability of autologous skin grafts for restoring integrity in large-scale defects, using bioprinted constructs as skin graft substitutes could offer an encouraging therapeutic alternative to conventional therapies for large-scale wounds, such as the transplantation of autologous tissue. Using layer-by-layer aggregation or volumetric bioprinting, inkjet bioprinting, laser-assisted bioprinting, or extrusion-based bioprinting, skin cells are deposited in a desired pattern. The resulting constructs may be used as skin graft substitutes to accelerate wound healing and reconstitute the physiological functions of the skin. In this review, we aimed to elucidate the current state of bioprinting within the context of skin tissue engineering and introduce and discuss different bioprinting techniques, possible approaches and materials, commonly used cell types, and strategies for graft vascularization for the production of bioprinted constructs for use as skin graft substitutes.