Multimaterial bioprinting technologies offer promising avenues to create mini-organ models with enhanced tissue heterogeneity and complexity. This article focuses on the application of three-dimensional bioprinting to fabricate organ-on-a-chip systems for in vitro drug testing and screening. We illustrate the capabilities and limitations of a bioprinting approach compared to microfabrication in constructing an organ-on-a-chip device. Further, we propose strategies in multimaterial integration for printing microphysiological tissue models. With these analyses, key challenges and future directions are highlighted.