Human heart (patho)physiology is now widely studied using human pluripotent stem cells, but the immaturity of derivative cardiomyocytes has largely limited disease modeling to conditions associated with mutations in cardiac ion channel genes. Recent advances in tissue engineering and organoids have, however, created new opportunities to study diseases beyond ''channelopathies.'' These synthetic cardiac structures allow quantitative measurement of contraction, force, and other biophysical parameters in three-dimensional configurations, in which the cardiomyocytes in addition become more mature. Multiple cardiac-relevant cell types are also often combined to form organized cardiac tissue mimetic constructs, where cell-cell, cell-extracellular matrix, and paracrine interactions can be mimicked. In this review, we provide an overview of some of the most promising technologies being implemented specifically in personalized heart-on-a-chip models and explore their applications, drawbacks, and potential for future development.