The complex development of the Indian Ocean over the past ~160 million years has involved massive magmatism, jumps in mid-ocean ridges stranding fragments of continents, and concomitant changing tectonic plate boundaries and configurations. Two of the three most active hotspots globally, Kerguelen and Réunion, have been closely involved in these processes and phenomena. Recent marine geoscientific investigations, in particular RV Investigator voyage IN2020_V01, have illuminated the tectonomagmatic evolution of the conjugate William’s Ridge (Kerguelen Plateau) and Broken Ridge, and next year’s RV Investigator voyage IN2027_V05 plans to examine the same for the Joey Rise, Roo Rise, and Zenith Plateau. These voyages have addressed and will tackle not only fundamental geoscientific problems, but also provide information with the potential to expand Australia’s marine jurisdiction under the United Nations Convention on the Law of the Sea. Specifically, in 2008, the UN’s Commission on the Limits of the Continental Shelf did not adopt the full continental shelf that Australia submitted for William’s Ridge and the Joey Rise due to insufficient available evidence. Australia has the option to make a new or revised submission for these two areas on the basis of data and samples acquired by the 2020 and 2027 RV Investigator voyages.