The goal of cardiac tissue engineering is to treat cardiovascular diseases through the implantation of engineered functional tissue replacements or the injection of cells and biomaterials, as well as to provide engineered cardiac constructs that can be used as an in vitro model of healthy or diseased heart tissues. This field is rapidly advancing with the new discoveries and improvements in stem cell technologies, materials science, and bioreactor design. In this review, some of the progress made in cardiac tissue engineering in the recent years, as well as the challenges that need to be overcome in future studies, will be discussed. The topics include the advances in engineering stem cell-derived cardiac tissues, the use of natural or synthetic polymers and decellularized organs as engineering scaffolds, the scaffold-free cell sheet engineering approach, the application of perfusion and mechanical or electrical stimulation in bioreactors, the organization of cardiac cells through microfabrication techniques, and the vascularization of engineered cardiac tissues in vitro and in vivo.