Perinatal Asphyxia—oxygen deficit at delivery—can lead to severe hypoxic ischaemic organ damage in newborns followed by a fatal outcome or severe life-long pathologies. The severe insults often cause neurodegenerative diseases, mental retardation and epilepsies. The mild insults lead to so-called “minimal brain-damage disorders” such as attention deficits and hyperactivity, but can also be associated with the development of schizophrenia and life-long functional psychotic syndromes. Asphyxia followed by re-oxygenation can potentially lead to development of several neurodegenerative pathologies, diabetes type 2 and cancer. The task of individual prediction, targeted prevention and personalised treatments before a manifestation of the life-long chronic pathologies usually developed by newborns with asphyxic deficits, should be given the extraordinary priority in neonatology and paediatrics. Socio-economical impacts of educational measures and advanced strategies in development of robust diagnostic approaches targeted at effected molecular pathways, biomarker-candidates and potential drug-targets for tailored treatments are reviewed in the paper.