The high attrition rate of drug candidates in clinical trials is often attributed to the use of conventional two-dimensional cell cultures and animal models that fail to accurately recapitulate human physiology. Three-dimensional (3D) bioprinting has emerged as a transformative technology for creating sophisticated, patient-relevant tissue models for drug screening and toxicity assessment. Concurrently, machine learning (ML) offers a powerful paradigm for extracting insights from complex, multi-modal data and optimizing intricate processes. This review presents a comprehensive and critical overview of the convergence of 3D bioprinting and ML, with a specific focus on their integrated applications in drug development. We systematically analyze the various data types generated throughout the bioprinting workflow, from process parameters and material properties to biological and 'omics' data. We then discuss the application of diverse ML approaches, from statistical methods to deep learning (DL), for optimizing bioprinting processes and enhancing the predictive accuracy of drug screening. By including specific quantitative outcomes and comparative analyses from recent studies, we provide an evidence-based perspective on the state of the field and highlight its potential to accelerate the drug discovery pipeline.