Myocardial infarction results from a blockage of a major coronary artery that shuts the delivery of oxygen and nutrients to a region of the myocardium, leading to massive cardiomyocytes death and regression of microvasculature. Growth factor and cell delivery methods have been attempted to revascularize the ischemic myocardium and prevent further cell death. Implantable cardiac tissue patches were engineered to directly revascularize as well as remuscularize the affected muscle. However, inadequate vascularization in vitro and in vivo limits the efficacy of these new treatment options. Breakthroughs in cardiac tissue vascularization will profoundly impact ischemic heart therapies. In this review, we discuss the full spectrum of vascularization approaches ranging from biological angiogenesis to microfluidic blood vessels as related to cardiac tissue engineering.