Within the first 28 days after birth, more than 1 in every 2500 newborns will suffer a stroke. The weekly-adjusted risk of stroke for a term-born infant is threefold higher than for a male smoker aged 50 to 59 years with hypertension and diabetes. Neonatal stroke has significant clinical and socio-economic consequences, leading to cerebral palsy, epilepsy, and a range of motor, sensory, and cognitive impairments. Currently, there is no treatment for the brain damage caused by neonatal stroke. In this review, we outline the differences in the complex interplay of inflammation, excitotoxicity, oxidative stress, and cell death after stroke between adults and neonates, which limits the direct transfer of knowledge between studies for understanding injury. We comprehensively document what is known about the pathophysiology of neonatal stroke and critically evaluate current therapeutic strategies, emphasising the urgent need for innovative treatments tailored to suit the neonatal brain. This analysis reveals that treatment with an injectable hydrogel scaffold, a three-dimensional, water-swollen polymer network, may be an innovative, viable approach to improve outcomes for infants suffering from the most severe forms of brain injury arising from neonatal stroke.