Despite increased use of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) for drug development and disease modeling studies, methods to generate large, functional heart tissues for human therapy are lacking. Here we present a "Cardiopatch" platform for 3D culture and maturation of hiPSC-CMs that after 5 weeks of differentiation show robust electromechanical coupling, consistent H-zones, I-bands, and evidence for T-tubules and M-bands. Cardiopatch maturation markers and functional output increase during culture, approaching values of adult myocardium. Cardiopatches can be scaled up to clinically relevant dimensions, while preserving spatially uniform properties with high conduction velocities and contractile stresses. Within window chambers in nude mice, cardiopatches undergo vascularization by host vessels and continue to fire Ca2+ transients. When implanted onto rat hearts, cardiopatches robustly engraft, maintain pre-implantation electrical function, and do not increase the incidence of arrhythmias. These studies provide enabling technology for future use of hiPSC-CM tissues in human heart repair.