Ischemic cardiac injury, arising due to myocardial infarction (MI), ischemia–reperfusion injury (IRI), and other ischemia-associated forms of cardiac damage, remains a major clinical challenge. The irreversible loss of cardiomyocytes from within the myocardium, together with oxidative stress and inflammation, creates a complex post-MI milieu that is not readily addressed by existing therapeutic strategies. Cardiac tissue engineering solutions that combine advanced biomaterials with either stem cell-derived cardiovascular cells, their derivatives (such as extracellular vesicles and exosomes), or other bioactive compounds (including chemokines and cytokines) are being developed to repair and regenerate the infarcted human heart. This review highlights the state-of-the-art strategies that utilize cutting-edge technologies to develop tissue-inducing biomaterial solutions for cardiac regeneration and repair, with particular emphasis on (i) integrating biomaterials with cells in strategies undergoing clinical investigation, (ii) incorporating cellular derivatives into biomaterial scaffolds, and (iii) designing and evaluating intrinsically functional biomaterials. This review aims to provide both a theoretical foundation and future perspectives for the innovation and optimization of next-generation tissue-inducing biomaterial-based strategies for cardiac tissue regeneration and repair.