Screening for effective therapeutic agents from millions of drug candidates is costly, time consuming, and often faces concerns due to the extensive use of animals. To improve cost effectiveness, and to minimize animal testing in pharmaceutical research, in vitro monolayer cell microarrays with multiwell plate assays have been developed. Integration of cell microarrays with microfluidic systems has facilitated automated and controlled component loading, significantly reducing the consumption of the candidate compounds and the target cells. Even though these methods significantly increased the throughput compared to conventional in vitro testing systems and in vivo animal models, the cost associated with these platforms remains prohibitively high. Besides, there is a need for three-dimensional (3D) cell-based drug-screening models which can mimic the in vivo microenvironment and the functionality of the native tissues. Here, we present the state-of-the-art microengineering approaches that can be used to develop 3D cell-based drug-screening assays. We highlight the 3D in vitro cell culture systems with live cell-based arrays, microfluidic cell culture systems, and their application to high-throughput drug screening. We conclude that among the emerging microengineering approaches, bioprinting holds great potential to provide repeatable 3D cell-based constructs with high temporal, spatial control and versatility.