Cardiovascular disease is the number one killer worldwide, with myocardial infarction (MI) responsible for approximately 1 in 6 deaths. The lack of endogenous regenerative capacity, added to the deleterious remodelling programme set into motion by myocardial necrosis, turns MI into a progressively debilitating disease, which current pharmacological therapy cannot halt. The advent of Regenerative Therapies over 2 decades ago kick-started a whole new scientific field whose aim was to prevent or even reverse the pathological processes of MI. As a highly dynamic organ, the heart displays a tight association between 3D structure and function, with the non-cellular components, mainly the cardiac extracellular matrix (ECM), playing both fundamental active and passive roles. Tissue engineering aims to reproduce this tissue architecture and function in order to fabricate replicas able to mimic or even substitute damaged organs. Recent advances in cell reprogramming and refinement of methods for additive manufacturing have played a critical role in the development of clinically relevant engineered cardiovascular tissues. This review focuses on the generation of human cardiac tissues for therapy, paying special attention to human pluripotent stem cells and their derivatives. We provide a perspective on progress in regenerative medicine from the early stages of cell therapy to the present day, as well as an overview of cellular processes, materials and fabrication strategies currently under investigation. Finally, we summarise current clinical applications and reflect on the most urgent needs and gaps to be filled for efficient translation to the clinical arena.