Heart disease is a major global health challenge and is one of the leading causes of morbidity and mortality worldwide. Significant research efforts have focused on elucidating its underlying mechanisms, developing novel therapeutic approaches, and advancing drug discovery methods. The emergence of induced pluripotent stem cells (iPSCs) has provided powerful tools for modeling cardiovascular diseases, enabling mechanistic studies, drug screening, and personalized treatment strategies. More recently, three-dimensional (3D) cardiac models, including organoids, engineered heart tissues, microfluidic chip platforms, and bioprinted constructs, have further advanced cardiac tissue modeling by offering physiologically relevant platforms for drug testing and disease modeling. This review highlights recent advances in diverse iPSC-derived 3D cardiac models for disease modeling, drug discovery, and high-throughput screening, with particular emphasis on 3D bioprinting technologies that enable the spatially controlled fabrication of multicellular, biomimetic cardiac tissues with tunable structural and functional properties. Specifically, we focus on key aspects of cardiac bioprinting, including printing modalities, the rheological and mechanical properties of bioinks, achievable printing resolution and cell density, strategies for vascularization, and post-printing tissue maturation. We also discuss the integration of cutting-edge technologies, including 3D cardiac models and artificial intelligence (AI)-driven analyses, to improve the predictive accuracy of these models. The development of iPSC-derived cardiac models, combined with emerging bioengineering and computational technologies, provides a platform for cardiovascular research. In particular, computational algorithms, including machine-learning and artificial-intelligence models, are increasingly being used in the assessment of drug-toxicity and cardiotoxicity, complementing these patient-specific experimental systems. Their applications in drug screening, cardiotoxicity assessment, and precision medicine may help accelerate therapeutic development and improve patient outcomes.