Seizures are the most common neurological emergencies in the neonatal period and are associated with poor neurodevelopmental outcomes. Seizures affect up to five per 1000 term births and population-based studies suggest that they occur even more frequently in premature infants. Seizures are a sign of an underlying cerebral pathology, the most common of which is hypoxic-ischaemic encephalopathy in term infants. Due to a growing body of evidence that seizures exacerbate cerebral injury, effective diagnosis and treatment of neonatal seizures is of paramount importance to reduce long-term adverse outcomes. Electroencephalography is essential for the diagnosis of seizures in neonates due to their subtle clinical expression, non-specific neurological presentation and a high frequency of electro-clinical uncoupling in the neonatal period. Hypoxic-ischaemic encephalopathy may require neuroprotective therapeutic hypothermia, accompanying sedation with opioids, anticonvulsant drugs or a combination of all of these. The efficacy, safety, tolerability and pharmacokinetics of seven anticonvulsant drugs (phenobarbital, phenytoin, levetiracetam, lidocaine, midazolam, topiramate and bumetanide) are reviewed. This review is focused only on studies reporting electrographically confirmed seizures and highlights the knowledge gaps that exist in optimal treatment regimens for neonatal seizures. Randomised controlled trials are needed to establish a safe and effective treatment protocol for neonatal seizures.