The development of the control of breathing begins in utero and continues postnatally. Fetal breathing movements are needed for establishing connectivity between the lungs and central mechanisms controlling breathing. Maturation of the control of breathing, including the increase of hypoxia chemosensitivity, continues postnatally. Insufficient oxygenation, or hypoxia, is a major stressor that can manifest for different reasons in the fetus and neonate. Though the fetus and neonate have different hypoxia sensing mechanisms and respond differently to acute hypoxia, both responses prevent deviations to respiratory and other developmental processes. Intermittent and chronic hypoxia pose much greater threats to the normal developmental respiratory processes. Gestational intermittent hypoxia, due to maternal sleep-disordered breathing and sleep apnea, increases eupneic breathing and decreases the hypoxic ventilatory response associated with impaired gasping and autoresuscitation postnatally. Chronic fetal hypoxia, due to biologic or environmental (i.e. high-altitude) factors, is implicated in fetal growth restriction and preterm birth causing a decrease in the postnatal hypoxic ventilatory responses with increases in irregular eupneic breathing. Mechanisms driving these changes include delayed chemoreceptor development, catecholaminergic activity, abnormal myelination, increased astrocyte proliferation in the dorsal respiratory group, among others. Long-term high-altitude residents demonstrate favorable adaptations to chronic hypoxia as do their offspring. Neonatal intermittent hypoxia is common among preterm infants due to immature respiratory systems and thus, display a reduced drive to breathe and apneas due to insufficient hypoxic sensitivity. However, ongoing intermittent hypoxia can enhance hypoxic sensitivity causing ventilatory overshoots followed by apnea; the number of apneas is positively correlated with degree of hypoxic sensitivity in preterm infants. Chronic neonatal hypoxia may arise from fetal complications like maternal smoking or from postnatal cardiovascular problems, causing blunting of the hypoxic ventilatory responses throughout at least adolescence due to attenuation of carotid body fibers responses to hypoxia with potential roles of brainstem serotonin, microglia, and inflammation, though these effects depend on the age in which chronic hypoxia initiates. Fetal and neonatal intermittent and chronic hypoxia are implicated in preterm birth and complicate the respiratory system through their direct effects on hypoxia sensing mechanisms and interruptions to the normal developmental processes. Thus, precise regulation of oxygen homeostasis is crucial for normal development of the respiratory control network. © 2021 American Physiological Society. Compr Physiol 11:1653-1677, 2021.