Cerebral palsy (CP) is the most prevalent, severe and costly motor disability of childhood. Consequently, CP is a public health priority for prevention, but its aetiology has proved complex. In this Review, we summarize the evidence for a decline in the birth prevalence of CP in some high-income nations, describe the epidemiological evidence for risk factors, such as preterm delivery and fetal growth restriction, genetics, pregnancy infection and other exposures, and discuss the success achieved so far in prevention through the use of magnesium sulfate in preterm labour and therapeutic hypothermia for birth-asphyxiated infants. We also consider the complexities of disentangling prenatal and perinatal influences, and of establishing subtypes of the disorder, with a view to accelerating the translation of evidence into the development of strategies for the prevention of CP.