Human heart failure due to myocardial infarction is a major health concern. The paucity of organs for transplantation limits curative approaches for the diseased and failing adult heart. Human induced pluripotent stem cell-derived cardiac myocytes (hiPSC-CMs) have the potential to provide a long-term, viable, regenerative-medicine alternative. Significant progress has been made with regard to efficient cardiac myocyte generation from hiPSCs. However, directing hiPSC-CMs to acquire the physiological structure, gene expression profile and function akin to mature cardiac tissue remains a major obstacle. Thus, hiPSC-CMs have several hurdles to overcome before they find their way into translational medicine. In this review, we address the progress that has been made, the void in knowledge and the challenges that remain. This article is part of a Special Issue entitled: Cardiomyocyte Biology: Integration of Developmental and Environmental Cues in the Heart edited by Marcus Schaub and Hughes Abriel.