Heart diseases are a leading cause of mortality worldwide. Terminally differentiated adult cardiomyocytes (CMs) lack the innate ability to regenerate. Their malfunction or significant loss can lead to conditions from cardiac arrhythmias to heart failure. For myocardial repair, cell- and gene-based therapies offer promising alternatives to donor organ transplantation. Human embryonic stem cells (hESCs) can self-renew while maintaining their pluripotency. Direct reprogramming of adult somatic cells to become pluripotent hES-like cells (also known as induced pluripotent stem cells or iPSCs) has been achieved. Both hESCs and iPSCs have been successfully differentiated into genuine human CMs. In this review, we describe our current knowledge of the structure-function properties of hESC/iPSC-CMs, with an emphasis on their electrophysiology and Ca(2+) handling, along with the hurdles faced and potential solutions for translating into clinical and other applications (e.g., disease modeling, cardiotoxicity and drug screening).