The occurrence of various forms of severe neurologic events has been increasingly reported in acute myocardial infarction patients receiving thrombolytic therapy. Strokes have long been known to complicate acute myocardial infarction. The recent attention on severe neurologic events has focused primarily on probable cerebral bleeds. The various forms of severe neurologic events that clinicians are confronted with have unique features and characteristics that will be delineated. The incidence of these events and patient risk factors for cerebral ischemia and cerebral hemorrhage will be outlined. Guidelines that should be adopted to minimize the chance of a patient's suffering a severe neurologic event while at the same time maximizing the number of patients who receive this lifesaving therapy are summarized.