The incidence of severe consequences of perinatal neonatal asphyxia and hypoxia-ischemic encephalopathy is still present despite the possibilities of modern technology and the growing education of health care staff. The consequences are numerous and include a wider range of clinical symptoms, ranging from mild neurodevelopment to severe forms of cerebral paralysis with severe cognitive-psychomotor retardation. One of the most dramatic side effects is certainly the death of a newborn. The positive neuroprotective effect of hypothermia has been known since ancient times and is used in neurosurgery and cardiac surgery. Thanks to the application of therapeutic hypothermia in the last twenty years, a great progress has been made in the treatment of asphyxiated newborns. In doing so, good selection of infants who meet the criteria for therapeutic hypothermia administration is extremely important in order to avoid possible unwanted complications, although in some cases they may be less dangerous than the potential benefits of therapeutic hypothermia treatment itself. This review paper presents the importance of the application of therapeutic hypothermia treatment in asphyxiated newborns, the algorithm of diagnostic tests, the procedure itself, its benefits and the final outcome in order to become an integral part of the treatment of asphyxiated newborns in as many Croatian maternity hospitals as possible.