Despite extensive breakthroughs in chemistry, molecular biology, and genetics in the last decades, the success rates of drug development projects remain low. To improve predictions of clinical efficacy and safety of new compounds, a plethora of 3D culture methods of human cells have been developed in which the cultured cells retain physiologically and functionally relevant phenotypes for multiple weeks. Here, we critically review current paradigms for organotypic cultures of human liver, gut, and kidney such as perfused microchips, spheroids, and hollow fiber bioreactors and discuss their utility for understanding drug pharmacokinetics, metabolism, and toxicity. Furthermore, bioprinting and the microfluidic integration of different tissue models to mimic systemic drug effects are highlighted as promising technological trends. In the last part of the review, we discuss important considerations regarding the choice of culture substratum material to limit adverse effects such as drug absorption while facilitating the phenotypic maintenance of cultured cells. We conclude that recent advances in organotypic and microphysiological culture models of human tissues can improve drug development and contribute to an amelioration of clinical attrition rates. However, further validation, benchmarking, and consolidation efforts are needed to achieve more widespread dissemination and eventually regulatory acceptance of these novel tools.