Abstract The integration of hierarchical, perfusable vasculature remains one of the most critical and unresolved challenges in engineering human cardiac tissues. Although substantial progress has been made in independently advancing myocardial and vascular tissue constructs, integrating both into a single functional platform remains a major barrier to translation. This review categorizes and evaluates two overarching strategies for engineering vascularized cardiac tissues: biologically driven approaches that leverage cell‐driven self‐organization, and engineering‐driven methods that impose tissue structure through biofabrication. Each strategy is examined in terms of its contributions to structural fidelity, functional maturation, and scalability, and a benchmarking framework is introduced to assess their physiological and translational relevance. Key insights are then synthesized to outline a path forward, with particular emphasis on the need for hybrid strategies that unite the complementary advantages of both approaches.