In vitro tissue/organ models are useful platforms that can facilitate systematic, repetitive, and quantitative investigations of drugs/chemicals. The primary objective when developing tissue/organ models is to reproduce physiologically relevant functions that typically require complex culture systems. Bioprinting offers exciting prospects for constructing 3D tissue/organ models, as it enables the reproducible, automated production of complex living tissues. Bioprinted tissues/organs may prove useful for screening novel compounds or predicting toxicity, as the spatial and chemical complexity inherent to native tissues/organs can be recreated. In this Review, we highlight the importance of developing 3D in vitro tissue/organ models by 3D bioprinting techniques, characterization of these models for evaluating their resemblance to native tissue, and their application in the prioritization of lead candidates, toxicity testing, and as disease/tumor models. Looking at the fine print: 3D bioprinting offers exciting prospects for printing 3D tissue/organ models. This technique can recreate the spatial and chemical complexity inherent to native tissues and organs. Hence, bioprinted tissues/organs have the potential to be useful in the prioritization of lead candidates, toxicity testing, and as disease/tumor models. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.