Myocardial infarction (MI) is a major source of morbidity and mortality worldwide, with over 7 million people suffering infarctions each year. Heart muscle damaged during MI is replaced by a collagenous scar over a period of several weeks, and the mechanical properties of that scar tissue are a key determinant of serious post-MI complications such as infarct rupture, depression of heart function, and progression to heart failure. Thus, there is increasing interest in developing therapies that modify the structure and mechanics of healing infarct scar. Yet most prior attempts at therapeutic scar modification have failed, some catastrophically. This article reviews available information about the mechanics of healing infarct scar and the functional impact of scar mechanical properties, and attempts to infer principles that can better guide future attempts to modify scar. One important conclusion is that collagen structure, mechanics, and remodeling of healing infarct scar vary so widely among experimental models that any novel therapy should be tested across a range of species, infarct locations, and reperfusion protocols. Another lesson from past work is that the biology and mechanics of healing infarcts are sufficiently complex that the effects of interventions are often counterintuitive; for example, increasing infarct stiffness has little effect on heart function, and inhibition of matrix metalloproteases (MMPs) has little effect on scar collagen content. Computational models can help explain such counterintuitive results, and are becoming an increasingly important tool for integrating known information to better identify promising therapies and design experiments to test them. Moving forward, potentially exciting new opportunities for therapeutic modification of infarct mechanics include modulating anisotropy and promoting scar compaction.