Once myocardium dies during a heart attack, it is replaced by scar tissue over the course of several weeks. The size, location, composition, structure, and mechanical properties of the healing scar are all critical determinants of the fate of patients who survive the initial infarction. While the central importance of scar structure in determining pump function and remodeling has long been recognized, it has proven remarkably difficult to design therapies that improve heart function or limit remodeling by modifying scar structure. Many exciting new therapies are under development but predicting their long-term effects requires a detailed understanding of how infarct scar forms, how its properties impact left ventricular function and remodeling, and how changes in scar structure and properties feed back to affect not only heart mechanics but also electrical conduction reflex hemodynamic compensations, and the ongoing process of scar formation itself. In this article, we outline the scar formation process following a myocardial infarction, discuss interpretation of standard measures of heart function in the setting of a healing infarct, then present implications of infarct scar geometry and structure for both mechanical and electrical function of the heart and summarize experiences to date with therapeutic interventions that aim to modify scar geometry and structure. One important conclusion that emerges from the studies reviewed here is that computational modeling is an essential tool for integrating the wealth of information required to understand this complex system and predict the impact of novel therapies on scar healing heart function, and remodeling following myocardial infarction.