Myocardial tissue engineering aims to repair, replace, and regenerate damaged cardiac tissue using tissue constructs created ex vivo. This approach may one day provide a full treatment for several cardiac disorders, including congenital diseases or ventricular dysfunction after myocardial infarction. Although the ex vivo construction of a myocardium-like tissue is faced with many challenges, it is nevertheless a pressing objective for cardiac reparative medicine. Multidisciplinary efforts have already led to the development of promising viable muscle constructs. In this article, we review the various concepts of cardiac tissue engineering and their specific challenges. We also review the different types of existing biografts and their physiological relevance. Although many investigators have favored cardiomyocytes, we discuss the potential of other clinically relevant cells, as well as the various hypotheses proposed to explain the functional benefit of cell transplantation.