The first Blalock-Taussig (BT) shunt was reported in 1944, and during the last 70 years, the procedure has evolved with the development of new materials and devices, and surgical approaches. It has, however, remained central to the palliation of neonates with complex congenital heart disease. The indications have expanded from the original aim of alleviating cyanosis and the pathophysiological results of chronic hypoxemia. They now include lesions with single ventricles, and rehabilitation of small pulmonary arteries. The physiology and hemodynamics of BT shunt circulations are very complex, and adverse hemodynamic events can be difficult to recognize. The consequences of shunt failure can be fatal, and the mortality (3–15%) and morbidity remain distressingly high even in the current era. Neonates undergoing BT shunt procedures or undergoing noncardiac surgery with this anatomy are challenging for the anesthesiologists to manage. There is a significant incidence of periprocedural cardiac arrest, often related to myocardial ischemia. A clear understanding of the anatomy and physiology is important. Any discussion of BT shunt in the current era has to include consideration of hypoplastic left heart syndrome and ‘single ventricle’ physiology.