The growth processes involved early in gestation and further into the intricate signaling networks in the brain form the basis for rapid cortical electrical bursting patterns. This leads to the quantification of cortical activity from the electroencephalogram (EEG) in full-term hypoxic infants and preterm infants. The associated neurological sequelae in both populations are foregrounded by a summary into current epidemiology and common clinical practices. The present review article highlights recent advances in physics and neuroscience, which will help in development of reliable predictors of outcome for full-term and preterm neonates after birth.