The promise of stem cells to repair the heart after damage or heart attack has not been realized because most such cells are lost after transplantation. A new approach is to grow substantial viable pieces of cardiac tissue from human stem cells by cardiac tissue engineering. Such constructs must be fully vascularized and perfused to ensure the viability of clinically relevant volumes of tissue. This requires careful choice of cells, culture conditions, a biomaterial to act as scaffold, and crucial strategies for vascularization. Autologous stem cells with high plasticity, which would avoid the need for antirejection therapies after transplantation, are an attractive source of both cardiomyocytes and vascular cells. Most stem cells also have inherent paracrine activity, releasing cytoprotective factors and growth-promoting cytokines that can further stimulate tissue regeneration and neovascularization through recruitment of endogenous stem and progenitor cells. Current advances for growing vascularized and functional cardiac constructs with human stem cells are described, bringing us a step closer to the engineering of complex cardiac tissues such as pacemaker, conducting tissue, or contractile myocardial flaps ideal for transplantation. From studies in rats successful transplantation of thin constructs to the ventricle has been reported, but there remain further issues to resolve before larger human constructs will be available to test in the clinic.