The aim of this review is to present 3D bioprinting of skin substitutes as an efficient approach of managing skin injuries. From a clinical point of view, classic treatments only provide physical protection from the environment, and existing engineered scaffolds, albeit acting as a physical support for cells, fail to overcome needs, such as neovascularisation. In the present work, the basic principles of bioprinting, together with the most popular approaches and choices of biomaterials for 3D-printed skin construct production, are explained, as well as the main advantages over other production methods. Moreover, the development of this technology is described in a chronological manner through examples of relevant experimental work in the last two decades: from the pioneers Lee et al. to the latest advances and different innovative strategies carried out lately to overcome the well-known challenges in tissue engineering of skin. In general, this technology has a huge potential to offer, although a multidisciplinary effort is required to optimise designs, biomaterials and production processes.