When initiating oral feedings, many preterm infants, compared to term newborns, have difficulty coordinating swallowing and breathing, making them at increased risk for aspiration. These are major clinical challenges that may prolong the Neonatal Intensive Care Unit (NICU) stay for otherwise healthy preterm infants. This review explores the impact of preterm birth on oral feeding and the development of a functional swallowing pump consisting of the brain, the multifunctional tongue and pharynx, and other oral structures. It also further examines the challenges preterm infants face coordinating swallowing with respiration. These issues present clinicians with assessment and treatment challenges.