The article is devoted to the analysis of the key conceptual aspects of the extraterritorial obligations of States under the scope of human rights treaties. To that end, some relevant provisions of regional and universal international treaties, as well as some international acts of the so called soft law, have been studied. The international human rights law provides for compliance of fundamental human rights and freedoms by States within and, in some cases, beyond their territory. The analysis from different angles (taking into account doctrinal and human rights perspectives) on this issue underlines that the extraterritorial State obligations derive from the relevant provisions of core international human rights treaties. © 2020, Springer Nature Switzerland AG.