Cardiac tissues generated from human induced pluripotent stem cells (iPSCs) can serve as platforms for patient-specific studies of physiology and disease1-6. However, the predictive power of these models is presently limited by the immature state of the cells1, 2, 5, 6. Here we show that this fundamental limitation can be overcome if cardiac tissues are formed from early-stage iPSC-derived cardiomyocytes soon after the initiation of spontaneous contractions and are subjected to physical conditioning with increasing intensity over time. After only four weeks of culture, for all iPSC lines studied, such tissues displayed adult-like gene expression profiles, remarkably organized ultrastructure, physiological sarcomere length (2.2 µm) and density of mitochondria (30%), the presence of transverse tubules, oxidative metabolism, a positive force-frequency relationship and functional calcium handling. Electromechanical properties developed more slowly and did not achieve the stage of maturity seen in adult human myocardium. Tissue maturity was necessary for achieving physiological responses to isoproterenol and recapitulating pathological hypertrophy, supporting the utility of this tissue model for studies of cardiac development and disease.