The adult heart is a vital and highly specialized organ of the human body, with limited capability of self-repair and regeneration in case of injury or disease. Engineering biomimetic cardiac tissue to regenerate the heart has been an ambition in the field of tissue engineering, tracing back to the 1990s. Increased understanding of human stem cell biology and advances in process engineering have provided an unlimited source of cells, particularly cardiomyocytes, for the development of functional cardiac muscle, even though pluripotent stem cell-derived cardiomyocytes poorly resemble those of the adult heart. This review outlines key biology-inspired strategies reported to improve cardiomyocyte maturation features and current biofabrication approaches developed to engineer clinically relevant cardiac tissues. It also highlights the potential use of this technology in drug discovery science and disease modeling as well as the current efforts to translate it into effective therapies that improve heart function and promote regeneration.