Regional fisheries management organisations (RFMOs) determine conservation measures for transboundary fisheries resources. They are also a forum for collective action toward the management of marine resources. One of the most complex and controversial aspects of this process is the allocation of catches between RFMO members. There are a variety of processes that can be used for catch allocation. In recent years, there has been a trend in some RFMOs towards establishing a system of criteria or indicators to determine the volume or percentage of catch that should be allocated to each RFMO member. Establishing such a system is challenging and the position of countries negotiating at RFMOs is also shaped by fisheries access arrangements. The debate on allocation has been ongoing at the Indian Ocean Tuna Commission for more than a decade, where one key point of disagreement is the treatment of historical catch taken in the waters of a coastal State. On the one hand, coastal states claim that catches historically taken in their exclusive economic zones (EEZ) should be attributed to them based on their sovereign rights over living resources. On the other, some fishing countries from outside the region claim catch history based on fishing conducted in the coastal State’s waters pursuant to access agreements. We analysed UNCLOS articles, publicly available fisheries access agreements, and national legislation to unpack the linkage between fisheries access arrangements and catch allocation discussions, and we also explored examples from other regions and RFMOs. We point out that the sovereign rights of coastal states over their EEZ provide a strong basis for allocation negotiations. In the absence of specific agreements to the contrary, any catch history that arises from foreign vessels fishing inside the EEZ should be attributed to the coastal State. We also argue that it is time for members of RFMOs—and especially of the Indian Ocean Tuna Commission—to move beyond the historical catch debate. They need to resolve their differences or consider other ways to allocate participatory rights in shared fisheries.