Models of heart disease and drug responses are increasingly based on human pluripotent stem cells (hPSCs) since their ability to capture human heart (dys-)function is often better than animal models. Simple monolayer cultures of hPSC-derived cardiomyocytes, however, have shortcomings. Some of these can be overcome using more complex, multi cell-type models in 3D. Here we review modalities that address this, describe efforts to tailor readouts and sensors for monitoring tissue- and cell physiology (exogenously and in situ) and discuss perspectives for implementation in industry and academia.Stem cells & developmental biolog