Up to 50% of patients presenting with ST elevation myocardial infarction (STEMI) are found to have multivessel coronary artery disease. These patients have a worse prognosis compared with the overall STEMI population. Two revascularization strategies are possible for these patients: treating the infarct-related artery percutaneous coronary intervention (IRA-PCI) only or achieving Complete revascularization (CR), either through an immediate multivessel PCI during the index angiography or during a second-staged procedure. Until recently, most clinical data on this issue were derived from observational studies – which all showed a clear advantage to the IRA-PCI over the CR approach. Over the past few years, several groundbreaking randomized trials have suggested that the CR approach may be at least equivalent, and perhaps superior, to the IRA-PCI strategy. This has caused a paradigm shift reflected in the recent US and European guidelines. However, there is still uncertainty on the optimal timing for achieving CR (immediate/during the index admission/during a subsequent elective admission) and several other important issues in terms of revascularization: the extent of revascularization needed to achieve maximal benefit, the optimal means to evaluate the significance of intermediate coronary stenosis in the context of acute myocardial infarction, and the best approach to treat chronic total occlusions have not been thoroughly examined, and are the subject of an ongoing debate.