Myocardial infarctions are one of the most common forms of cardiac injury and death worldwide. Infarctions cause immediate necrosis in a localized region of the myocardium, which is followed by a repair process with inflammatory, proliferative, and maturation phases. This repair process culminates in the formation of scar tissue, which often leads to heart failure in the months or years after the initial injury. In each reparative phase, the infarct microenvironment is characterized by distinct biochemical, physical, and mechanical features, such as inflammatory cytokine production, localized hypoxia, and tissue stiffening, which likely each contribute to physiological and pathological tissue remodeling by mechanisms that are incompletely understood. Traditionally, simplified two-dimensional cell culture systems or animal models have been implemented to elucidate basic pathophysiological mechanisms or predict drug responses following myocardial infarction. However, these conventional approaches offer limited spatiotemporal control over relevant features of the post-infarct cellular microenvironment. To address these gaps, Organ on a Chip models of post-infarct myocardium have recently emerged as new paradigms for dissecting the highly complex, heterogeneous, and dynamic post-infarct microenvironment. In this review, we describe recent Organ on a Chip models of post-infarct myocardium, including their limitations and future opportunities in disease modeling and drug screening.