Bioprinting technologies are powerful additive biofabrication techniques to produce cellular constructs for skin tissue engineering owing to their unique ability to precisely pattern living and non-living materials in pre-defined spatial locations. This unique feature, combined with the computer controlled printing and medical imaging techniques, enable researchers and clinicians to generate patient specific constructs partly replicating the intricate compositional and architectural organization of the skin. Bioprinting has been used to automatically dispense hydrogels with skin cells located in prescribed sites that promote skin formation in vitro and in vivo. Current skin bioprinting approaches mostly rely on the sequential printing of fibroblasts and keratinocytes embedded within a homogeneous hydrogel. Although such approaches have already been translated to pre-clinical scenarios, they still present limitations in terms of fully replicating the cellular and extracellular matrix (ECM) heterogeneity in native skin. The success of bioprinting for skin repair strongly depends on the design of printable bioinks capable of supporting the function of printed cells and stimulating the production of new ECM components. To better mimic the human skin, novel developments in dedicated bioprinting technologies, in the design of bioinks, as well as in the printing of vascularised constructs are necessary. This paper presents an overview regarding the use of bioprinting for skin tissue engineering applications. The operating principles of bioprinting technologies are outlined along with requirements of printed skin constructs. Finally, pre-clinical results are summarized and future perspectives for the field are highlighted.