Anesthesia in premature infants is a much greater challenge than in full-term newborns, mainly because of the immaturity of their metabolism and organ systems. This significantly affects the pharmacokinetics and pharmacodynamics of anesthetic drugs. Underdeveloped lungs, caused by a lack of endogenous surfactant, together with a reduced functional residual capacity, increase the risk of hypoxemia, ventilator-induced lung injury, and reversal of fetal circulation. Last but not least, thermomanagement is essential. This interactive algorithm guides the solver through the comprehensive care of a preterm newborn from the anesthesiologist’s perspective — from preoperative preparation, through anesthesia management and perioperative complication handling, to the safe handover of the patient to the destination unit.