Basic biology research and drug development rely heavily on simple in vitro assays in a dish, and on in vivo animal studies. These models do not recapitulate human physiology, thus have poor predictive value. Microphysiological systems and organs-on-chips promise to accelerate biomedical and pharmaceutical research by providing more authentic in vitro replicas of human tissues. We present a modular heart-on-chip system based on engineered human stem cell-derived cardiac muscle tissues that recapitulate the laminar structure of the native ventricle. This system primarily provides continuous functional readouts of contractile stress and beat rate of the engineered cardiac tissue. These readouts can be combined with simultaneous electrophysiological measurements such as membrane potential or calcium imaging. Additionally, these cardiac tissues can be coupled with endothelial barriers to mimic the interface with the blood vessel that nourishes the tissue. We demonstrate the use of this platform for disease modeling and for toxicology and drug-testing purposes.