Bioprinting is reshaping the field of tissue regeneration and drug screening by creating physiologically accurate and scalable tissue models that reduce the limitations of conventional animal testing. It helps to minimize interspecies variability by developing complex 3D tissue structures that closely mimic the structural and functional characteristics of native tissues, ensuring high reproducibility. Furthermore, it supports more humane and sustainable preclinical testing by aligning with the ethical 3Rs principles (Replacement, Reduction and Refinement). Although bioprinting offers many advantages, its full potential in evaluating drug testing applications has yet to be harnessed. In this review, we discuss the efficacy of key bioprinting techniques in replicating the structural and functional characteristics of engineered tissues, comparing them with their native counterparts. Further, we highlight case studies demonstrating the applications of bioprinted skin, cardiac, hepatic, renal, bone, and cancer models in pharmaceutical research. The commercialization of bioprinted drug testing platforms and their integration into pharmaceutical development are also discussed. Finally, we outline key advantages, current challenges, and future directions needed to establish bioprinting as a transformative tool for preclinical drug testing, aiming to replace traditional animal models.