Forced migration processes, which started in Ukraine with the collapse of the Soviet Union, have taken new forms and reached their peak with the aggression of the Russian Federation in 2014. Since then, the problem of determining the impact of these processes on the development and security of the country's regions has been particularly relevant. In this regard, the article considers existing methods and international experience of a quantitative assessment of the impact of migration phenomena on the socio-economic development of regions. In addition, the author pays special attention to the identification and justification of the features inherent in internal migration processes, which directly impose restrictions on the quantitative assessment of the impact of these phenomena on the socio-economic development of regions and the obstacles researchers face in this field. Several critical features are determining the requirements for the choice of quantitative methods for assessing the impact of migration processes on regional socio-economic development, i.e., the complexity of establishing a direct relationship resulting from displacement is completely separated from the general societal changes; the impact of displacement will vary depending on several key factors; a high level of subjective judgements and estimations; the research results are sensitive to the level of initial data aggregation, their homogeneity and comparability; the lack of statistical information must be taken into account. A retrospective analysis of existing domestic and foreign approaches to overcome these problems has been carried out. Moreover, their advantages and disadvantages are pointed out. Based on the obtained results, it has been proved that the linear paradigm, which is superior to the classical economic and mathematical methods, is not always applicable. At the same time, the possibility of using modern non-linear approaches such as the theory of open systems, the theory of chaos has been proposed and justified. Furthermore, relevant conclusions have been made, and prospects for further research have been outlined.
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