Postnatal ductal closure is stimulated by rising oxygen tension and withdrawal of vasodilatory mediators (prostaglandins, nitric oxide, adenosine) and by vasoconstrictors (endothelin-1, catecholamines, contractile prostanoids), ion channels, calcium flux, platelets, morphologic maturity, and a favorable genetic predisposition. A persistently patent ductus arteriosus (PDA) in preterm infants can have clinical consequences. Decreasing pulmonary vascular resistance, especially in extremely low gestational age newborns, increases left-to-right shunting through the ductus and increases pulmonary blood flow further, leading to interstitial pulmonary edema and volume load to the left heart. Potential consequences of left-to-right shunting via a hemodynamically significant patent ductus arteriosus (hsPDA) include increased risk for prolonged ventilation, bronchopulmonary dysplasia, necrotizing enterocolitis or focal intestinal perforation, intraventricular hemorrhage, and death. In the last decade, there has been a trend toward less aggressive treatment of PDA in preterm infants. However, there is a subgroup of infants who will likely benefit from intervention, be it pharmacologic, interventional, or surgical: (1) prophylactic intravenous indomethacin in highly selected extremely low gestational age newborns with PDA (<26 + 0/7 weeks’ gestation, <750 g birth weight), (2) early targeted therapy of PDA in selected preterm infants at particular high risk for PDA-associated complications, and (3) PDA ligation, catheter intervention, or oral paracetamol may be considered as rescue options for hsPDA closure. The impact of catheter-based closure of hsPDA on clinical outcomes should be determined in future prospective studies. Finally, we provide a novel treatment algorithm for PDA in preterm infants that integrates the several treatment modalities in a staged approach.