Brain injury in preterm newborn infants is often attributed to hypoxia–ischemia even when neither hypoxia nor ischemia is documented, and many causative speculations are based on the same assumption. We review human and animal study contributions with their strengths and limitations, and conclude that – despite all the work done in human fetal neuropathology and developmental models in animals – the evidence remains unconvincing that hypoxemia, in the fetus or newborn infant, contributes appreciably to any encephalopathy of prematurity. Giving an inappropriate causal name to a disorder potentially limits the options for change, should our understanding of the etiologies advance. The only observationally‐based title we think appropriate is ‘encephalopathy of prematurity’. Future pathophysiological research should probably include appropriately designed epidemiology studies, highly active developmental processes, infection and other inflammatory stimuli, the immature immune system, long chain fatty acids and their transporters, and growth (neurotrophic) factors. What this paper adds Fetal hypoxemia is rarely documented in brain injury studies. Animal studies fail to consider human–animal fetal anatomical differences. Putative treatments from animal models have not found clinical use. Observational studies constitute the only approach to etiological understanding. No convincing evidence yet that hypoxemia injures preterm brain. Encephalopathy of prematurity is preferable to hypoxia‐ischemia as a term for this disorder. Encephalopathy of prematurity is preferable to hypoxia‐ischemia as a term for this disorder.