Cardiovascular organ-on-a-chip (OoC) devices are composed of engineered or native functional tissues that are cultured under controlled microenvironments inside microchips. These systems employ microfabrication and tissue engineering techniques to recapitulate human physiology. This review focuses on human OoC systems to model cardiovascular diseases, to perform drug screening, and to advance personalized medicine. We also address the challenges in the generation of organ chips that can revolutionize the large-scale application of these systems for drug development and personalized therapy.