Tissue engineering combines principles of engineering and biology to generate living tissue equivalents for drug testing, disease modeling, and regenerative medicine. As techniques for reprogramming human somatic cells into induced pluripotent stem cells (iPSCs) and subsequently differentiating them into cardiomyocytes and other cardiac cells have become increasingly efficient, progress toward the development of engineered human cardiac muscle patch (hCMP) and heart tissue analogs has accelerated. A few pilot clinical studies in patients with post-infarction LV remodeling have been already approved. Conventional methods for hCMP fabrication include suspending cells within scaffolds, consisting of biocompatible materials, or growing two-dimensional sheets that can be stacked to form multilayered constructs. More recently, advanced technologies, such as micropatterning and three-dimensional bioprinting, have enabled fabrication of hCMP architectures at unprecedented spatiotemporal resolution. However, the studies working on various hCMP-based strategies for in vivo tissue repair face several major obstacles, including the inadequate scalability for clinical applications, poor integration and engraftment rate, and the lack of functional vasculature. Here, we review many of the recent advancements and key concerns in cardiac tissue engineering, focusing primarily on the production of hCMPs at clinical/industrial scales that are suitable for administration to patients with myocardial disease. The wide variety of cardiac cell types and sources that are applicable to hCMP biomanufacturing are elaborated. Finally, some of the key challenges remaining in the field and potential future directions to address these obstacles are discussed.