New Zealand's fisheries are perhaps best known for the individual transferable quota (ITQ) system brought about by the Fisheries Amendment Act 1986. The 1986 Act allocated quota to fishing firms and individuals that met the allocation criteria. Part-time fishers, many of whom were Maori, New Zealand's indigenous people, were excluded from the initial allocation. The 1986 Act did not address claims by Maori of having indigenous rights guaranteed by the Treaty of Waitangi 1840. Since the Treaty, Maori have protested against government actions and legislation that have eroded their rights guaranteed by the Treaty. The implementation of the 1986 Act prompted further Treaty-based claims to large areas of fisheries, and the ITQ system was used to settle several claims. This paper explores Maori views on resource use and claims to fisheries resources, legislative changes enacted to settle Maori fisheries claims, and claims that remain outstanding. The insights of this paper have relevance to the broader discussion on the position of indigenous peoples throughout the world.