This contribution explores whether and how international law applies to disputed maritime zones by examining the Falklands (Malvinas) dispute between the UK and Argentina as a case study. After briefly outlining some of the maritime aspects of the bilateral dispute, the article assesses whether a bilateral investment treaty between Argentina/the UK and the investor's home State would cover investments located in the maritime areas adjacent to the Islands. In studying this issue, attention will be paid to, inter alia, the scope of treaties ratione loci, State practice in relation to overseas territories, the application of treaties to activities in the exclusive economic zone and the continental shelf, and select challenges that could arise in the context of investor-State arbitration.