Engineering functional human cardiac tissue that mimics the native adult morphological and functional phenotype has been a long held objective. In the last 5 years, the field of cardiac tissue engineering has transitioned from cardiac tissues derived from various animal species to the production of the first generation of human engineered cardiac tissues (hECTs), due to recent advances in human stem cell biology. Despite this progress, the hECTs generated to date remain immature relative to the native adult myocardium. In this review, we focus on the maturation challenge in the context of hECTs, the present state of the art, and future perspectives in terms of regenerative medicine, drug discovery, preclinical safety testing and pathophysiological studies.