Cardiovascular disease is a leading cause of death worldwide, necessitating the development of effective treatment strategies. A myocardial infarction involves the blockage of a coronary artery leading to depletion of nutrient and oxygen supply to cardiomyocytes and massive cell death in a region of the myocardium. Cardiac tissue engineering is the growth of functional cardiac tissue in vitro on biomaterial scaffolds for regenerative medicine application. This strategy relies on the optimization of the complex relationship between cell networks and biomaterial properties. In this review, we discuss important biomaterial properties for cardiac tissue engineering applications, such as elasticity, degradation, and induced host response, and their relationship to engineered cardiac cell environments. With these properties in mind, we also emphasize in vitro use of cardiac tissues for high-throughput drug screening and disease modelling.