Whether the European home states of transnational corporations (TNCs) are responsible for the TNCs’ impacts abroad under the European Convention on Human Rights (ECHR) is an important and topical question. The first pillar of the UN Framework on business and human rights (B&HR) comprises the ‘state duty to protect’ against business-related human rights abuses. The second of the United Nations Guiding Principles maintains that, ‘States should set out clearly the expectation that all business enterprises domiciled in their territory and/or jurisdiction respect human rights throughout their operations’. Originally, authority for the ‘state duty to protect’ was drawn from UN treaty body commentaries. Subsequently, however, scholars have concluded that a home state duty to regulate TNCs abroad already exists as a matter of human rights law, with reference to decisions of the European Court of Human Rights (ECtHR). Accordingly, this chapter scrutinizes the case for a home state duty to regulate TNCs’ extraterritorial human rights impacts under the ECHR and reviews rules and parameters of extraterritorial jurisdiction under the Convention with reference to decided cases. Having considered recent Council of Europe B&HR policy in which the issue of extraterritoriality is addressed, it offers concluding reflections on the possible significance of the exterritorial duty debate for the wider B&HR field.