The emergence of human induced pluripotent stem cells (hiPSCs) and efficient differentiation of hiPSC-derived cardiomyocytes (hiPSC-CMs) induced from diseased donors have the potential to recapitulate the molecular and functional features of the human heart. Although the immaturity of hiPSC-CMs, including the structure, gene expression, conduct, ion channel density, and Ca2+ kinetics, is a major challenge, various attempts to promote maturation have been effective. Three-dimensional cardiac models using hiPSC-CMs have achieved these functional and morphological maturations, and disease models using patient-specific hiPSC-CMs have furthered our understanding of the underlying mechanisms and effective therapies for diseases. Aside from the mechanisms of diseases and drug responses, hiPSC-CMs also have the potential to evaluate the safety and efficacy of drugs in a human context before a candidate drug enters the market and many phases of clinical trials. In fact, novel drug testing paradigms have suggested that these cells can be used to better predict the proarrhythmic risk of candidate drugs. In this review, we overview the current strategies of human engineered heart tissue models with a focus on major cardiac diseases and discuss perspectives and future directions for the real application of hiPSC-CMs and human engineered heart tissue for disease modeling, drug development, clinical trials, and cardiotoxicity tests.