Skin tissue damage is a major challenge and a burden on healthcare systems, from burns and other trauma to diabetes and vascular disease. Although the biological complexities are relatively well understood, appropriate repair mechanisms are scarce. Three-dimensional bioprinting is a layer-based approach to regenerative medicine, whereby cells and cell-based materials can be dispensed in fine spatial arrangements to mimic native tissue. Various bioprinting techniques have been employed in wound repair-based skin tissue engineering, from laser-induced forward transfer to extrusion-based methods, and with the investigation of the benefits and shortcomings of each, with emphasis on biological compatibility and cell proliferation, migration, and vitality. Development of appropriate biological inks and the vascularization of newly developed tissues remain a challenge within the field of skin tissue engineering. Progress within bioprinting requires close interactions between material scientists, tissue engineers, and clinicians. Microvascularization, integration of multiple cell types, and skin appendages will be essential for creation of complex skin tissue constructs.