The main issue addressed in the article is the question of the applicability of criminal law over time and space. This issue covers several aspects: first, issues related to the retroactive effect of criminal law, its application in retrospect, and the relationship between the principles of legality and justice; second, issues concerning the application of criminal law on the international stage, problems of extradition, human rights, and legal conflicts arising from the interaction of different legal systems in a globalized world. The article also discusses issues related to international cooperation in criminal justice and the application of law to actions committed beyond the borders of one country. The objective of the article is to analyze the main problems of legal regulation regarding the application of criminal law over time and space, as well as to propose possible solutions to these problems. The task of the article is to identify the key problems arising in the application of criminal legislation and propose recommendations for improving the legal mechanisms that ensure fair and effective justice in the context of globalization and changing social relations. To achieve the goal, several methods were used in the research. The main methods were comparative, analytical, and legal. The comparative method allowed for the study of different approaches to regulating the issue of the applicability of criminal law in different countries, revealing differences in national legal systems. The analytical method was used to examine judicial practice and to identify key problems arising from the application of criminal law over time and space. The legal method was used to analyze current legislative norms and international conventions, as well as to assess their effectiveness in the context of legal conflicts and human rights. The research results show that the main problems in the application of criminal law over time are related to the difficulty of balancing the principles of legality and justice, especially in the context of its retroactive effect. Issues concerning the application of criminal law over space are also relevant, particularly in light of the rise in transnational crime and the need for international cooperation. At the same time, the key issues are extradition, human rights, and the protection of citizens in international jurisdictions. Problems of legal conflicts between different legal systems also remain significant, especially in the context of globalization and the mobility of citizens. The significance of these results lies in the fact that they contribute to a deeper understanding of the legal and ethical issues that arise when applying criminal law in modern conditions. Recommendations for improving international cooperation, legal mechanisms for extradition, and the legal protection of the accused can help create a fairer and more effective legal system capable of accounting for changes in social conditions and international realities.