Most current drug screening assays used to identify new drug candidates are 2D cell-based systems, even though such in vitro assays do not adequately recreate the in vivo complexity of 3D tissues. Inadequate representation of the human tissue environment during a preclinical test can result in inaccurate predictions of compound effects on overall tissue functionality. Screening for compound efficacy by focusing on a single pathway or protein target, coupled with difficulties in maintaining long-term 2D monolayers, can serve to exacerbate these issues when utilizing such simplistic model systems for physiological drug screening applications. Numerous studies have shown that cell responses to drugs in 3D culture are improved from those in 2D, with respect to modeling in vivo tissue functionality, which highlights the advantages of using 3D-based models for preclinical drug screens. In this review, we discuss the development of microengineered 3D tissue models which accurately mimic the physiological properties of native tissue samples, and highlight the advantages of using such 3D micro-tissue models over conventional cell-based assays for future drug screening applications. We also discuss biomimetic 3D environments, based-on engineered tissues as potential preclinical models for the development of more predictive drug screening assays for specific disease models.