Significant advances in perinatal and neonatal medicine over the last 20 years and the recent emergence of fetal surgery has resulted in anesthesia providers caring for a growing number of infants born at the margin of viability. Anesthetic management in this patient population has to take into consideration the immature function of many vital organ systems as well as the effects of the underlying disease processes, which can frequently lead to severe physiological derangements. Accordingly, premature infants presenting for major surgeries early in life can represent a significant anesthetic challenge. However, even with advanced anesthetic and surgical management and optimal intensive care, extremely premature infants face substantial postoperative morbidity and mortality, as well as prolonged hospital courses. In this article, we will discuss the following questions: How far have we come in improving outcomes of extreme prematurity? And what will the future medical and societal challenges be, as we continue to redefine the limits of viability?