The theoretic fundamentals of the geography of extremal situations as a new approach for environmental science and socio-economic investigations are disclosed. The new direction of research named the geography of extreme situations is substantiated. The formation of the extreme operating mode in socio-ecological-economic systems (landscapes) that have a destructive, unbalanced nature and lead to imbalances in their development is explored. The term «geography of extreme situations» is introduced to determine the particular area of geographical knowledge, which studies natural and socio-economic phenomena that have the character of fast imbalance. The methodical approaches to investigation of the extremeness level of the territory via the example of Ukraine and the European Union are shown. In geography this approach was applied only to determine the specific features of the influence of natural conditions on human activity. The indicators of environmental disasters that include the amount of pollutant emissions into the atmosphere, the discharge of contaminated sewage into the natural surface water, the degradation of soil resources, the reduction of the forest fund, the species diversity of flora and fauna are disclosed. The different indices of extremeness such as medical and demographic, socioeconomic, engineering, physical-geographical and others are proposed.