[7] The traditional lands of the Diyari were estimated by Norman Tindale to have encompassed roughly 8,400 square miles (22,000 km2),[8] and lay in the delta of the Barcoo River (Cooper Creek) to the east of Lake Eyre.
[12][13] Lorimer Fison (1880): After the creation, brothers, sisters, and others of the closest kin, intermarried promiscuously, until — the evil effects of these alliances becoming manifest — a council of the chiefs was assembled to consider in what way they might be averted, the result of their deliberations being a petition to the Muramura (Good Spirit), in answer to which he ordered that the tribe should be divided into branches, and distinguished one from another by different names, after objects animate and inanimate, such as dogs, mice, emu, rain, iguana, and so forth; the members of any such branch not to intermarry, but with permission for one branch to mingle with another.
[b][14][15]The Diyari creation story imagined Mooramoora, the good spirit, making small black lizards at first, and delighted with them, they decided should hold sway over all other created beings.
Man could not run down the fleet, tasty emu, and the deity was asked to make heat so that it would tire and allow men to catch up and trap it.
[10] The Diyari foundational myths stated that originally man was incestuously promiscuous, fathers, mothers, sons and daughter all marrying each other.
[18] Before the white intrusion on their lands made its impact, the Dieri were divided into two tribal groups, the Ku'na:ri around Cooper Creek and the Pandu in proximity of Lake Hope.
[12] The Dieri Aboriginal Corporation (DAC) incorporated in 2001 and by 2014 had 600 members living in Marree, Lyndhurst, Port Augusta, Whyalla and in Broken Hill in New South Wales.
In May 2012 The Federal Court of Australia made a determination which recognised Diyari rights to 47,000 square kilometres (18,000 sq mi) of land along Cooper Creek, with boundaries extending to part of the Strzelecki Regional Reserve and the Lake Eyre National Park.