Tissue engineering is well suited for the treatment of cardiac disease due to the limited regenerative capacity of native cardiac tissue and the loss of function associated with endemic cardiac pathologies, such as myocardial infarction and congenital heart defects. However, the physiological complexity of the myocardium imposes extensive requirements on tissue therapies intended for these applications. In recent years, the field of cardiac tissue engineering has been characterized by great innovation and diversity in the fabrication of engineered tissue scaffolds for cardiac repair and regeneration to address these problems. From early approaches that attempted only to deliver cardiac cells in a hydrogel vessel, significant progress has been made in understanding the role of each major component of cardiac living tissue constructs (namely cells, scaffolds, and signaling mechanisms) as they relate to mechanical, biological, and electrical in vivo performance. This improved insight, accompanied by modern material science techniques, allows for the informed development of complex scaffold materials that are optimally designed for cardiac applications. This review provides a background on cardiac physiology as it relates to critical cardiac scaffold characteristics, the degree to which common cardiac scaffold materials fulfill these criteria, and finally an overview of recent in vivo studies that have employed this type of approach.