The constantly evolving domain of pharmaceutical research necessitates the discovery, development, and screening of novel drugs. Most of the drugs that successfully pass preclinical drug screening encounter failure during clinical trials, primarily attributed to the inadequacies of prevailing drug screening systems. The conventional two-dimensional (2D) drug screening models and animal studies are inadequate mainly due to their inability to mimic the in vivo architecture of human organs. Three-dimensional (3D) constructs with human cells exhibit notable advantages over traditional 2D screening systems, making them a more promising model for drug screening. The development of more sophisticated and innovative additive manufacturing technology led to the 3D printing of live tissue constructs, known as 3D bioprinting where the tissue organisation of the human body can be replicated. Various 3D bio-printed organ models, including liver, heart, lungs, kidney, skin, intestine, and bone, are currently being developed using additive manufacturing technology and evaluated for testing the efficacy of drugs for various applications. Disease models are also being constructed for the preclinical examination of drugs or for the personalised therapies. In this chapter, an overview of the utilisation of additively manufactured products will be discussed with particular emphasis on the bioinks and techniques employed for the development of different 3D bio-printed tissue constructs for drug testing. The challenges faced by the technique, as well as the critical outlooks and future advancements, will be discussed.