In the modern world, myocardial infarction is one of the most common cardiovascular diseases, which are responsible for around 18 million deaths every year or almost 32% of all deaths. Due to the detrimental effects of COVID-19 on the cardiovascular system, this rate is expected to increase in the coming years. Although there has been some progress in myocardial infarction treatment, translating pre-clinical findings to the clinic remains a major challenge. One reason for this is the lack of reliable and human representative healthy and fibrotic cardiac tissue models that can be used to understand the fundamentals of ischemic/reperfusion injury caused by myocardial infarction and to test new drugs and therapeutic strategies. In this review, we first present an overview of the anatomy of the heart and the pathophysiology of myocardial infarction, and then discuss the recent developments on pre-clinical infarct models, focusing mainly on the engineered three-dimensional cardiac ischemic/reperfusion injury and fibrosis models developed using different engineering methods such as organoids, microfluidic devices, and bioprinted constructs. We also present the benefits and limitations of emerging and promising regenerative therapy treatments for myocardial infarction such as cell therapies, extracellular vesicles, and cardiac patches. This review aims to overview recent advances in three-dimensional engineered infarct models and current regenerative therapeutic options, which can be used as a guide for developing new models and treatment strategies.