The unique differentiation program of the ductus arteriosus (DA) is essential for its specific task during fetal life and for the adapting circulation after birth. Phenotypic changes occur in the DA during the normal maturation and definitive closure. Morphological abnormalities of the vessel wall characterize the persistent DA (PDA) in older children. Here, we give an overview of the animal models of DA regulation and remodeling. Genetic research has identified the cause of syndromic forms of PDA, such as the TFAP2B mutations in Char syndrome. Genes that interfere with the remodeling of vascular smooth muscle cells (VSMCs) of the ductal media are affected in virtually all of these anomalies. Therefore, the pivotal regulatory role of VSMCs is emphasized. A better understanding of the genetic background of this developmental process may help develop new strategies to manipulate the DA in premature infants, neonates with duct-dependent anomalies, and patients with syndromic and non-syndromic PDA.