Based on the 3D printing technologies and the concepts developed in tissue engineering during the last decades, 3D bioprinting is emerging as the most innovative and promising technology for the generation of human tissues and organs. In the case of skin bioprinting, thanks to the research process carried out during the last years, interfollicular skin has been printed with a structural and functional quality that paves the way for clinical and industrial applications. This review analyzes the present achievements and the future improvements that this area must bring about if bioprinted skin is to become widely used. We have made an effort to integrate the technological and the biological/biomedical sides of the subject.