The Martu people are connected through shared country as well as through a common language, Martu Wangka (Martu talk).

Martu Wangka is a recent amalgamation of several dialects, such as Kartujarra, Putijarra, Mandiljarra, that were spoken in discrete parts of the Martu lands.

In the eastern part of the determination area, the Tarlka Matuwa Piarku Martu peoples have an ancestral connection to the area.

In the western determination area, traditionally associated with the western desert, the people (mostly from the north-east) migrated to the area from approximately 1925-1975, and rights were acquired to this area consistent to the Traditional Law and Custom.

Matuwa Kurrara Kurrara National Park and nature reserve at Lake Carnegie was created on 5 May 2023. It combines the existing IPA dedicated in 2015, with 2 former pastoral leases and creates an additional nature reserve.

It contains sacred water sites — the junu (waterhole), karo (creeks), pilkililli (claypans) are precious. Jukurrpa (Dreaming) sites and Jukurrpa tjina (Dreaming tracks) connect Matuwa and Kurrara Kurrara to the desert country across Western Australia, the Northern Territory and South Australia and to many other desert IPAs.