Cardiovascular diseases are prevalent worldwide and are the most frequent causes of death in the United States. Although spending in drug discovery/development has increased, the amount of drug approvals has seen a progressive decline. Particularly, adverse side effects to the heart and general vasculature have become common causes for preclinical project closures, and preclinical models do not fully recapitulate human in vivo dynamics. Recently, organs-on-a-chip technologies have been proposed to mimic the dynamic conditions of the cardiovascular system—in particular, heart and general vasculature. These systems pay particular attention to mimicking structural organization, shear stress, transmural pressure, mechanical stretching, and electrical stimulation. Heart- and vasculature-on-a-chip platforms have been successfully generated to study a variety of physiological phenomena, model diseases, and probe the effects of drugs. Here, we review and discuss recent breakthroughs in the development of cardiovascular organs-on-a-chip platforms, and their current and future applications in the area of drug discovery and development.