What does the United States look like, and who gets to decide? Our museums of modern and contemporary art, after far too long, have at last begun to esteem the work of living Native American artists — and several major shows, including the Whitney Museum of American Art’s just-opened biennial, have plunged into the ruinous legacy of settler colonialism in contemporary society.

Recent biennials in New Mexico and Hawaii, states with sizable Native populations, have also pushed for a greater place for Indigenous people in today’s art world. In some cases, debates over the presence of Native Americans in museums have come without warning; in 2017, at the Walker Art Center in Minneapolis, objections from Dakota people to Sam Durant’s public sculpture “Scaffold” led the artist to disclaim the work and approve its dismantlement.

How to move forward, and build a common artistic future on stolen land? As American curators and artists get serious about unwinding the colonial legacies embedded in our views of modern art, another country can offer a primer: Australia, where debates on the “contemporaneity” of Indigenous art predate ours by decades.

Two shows in New York offer profoundly different views of art from Indigenous Australia, and establish the stakes for exhibiting work made very far from our white cubes. At Gagosian through July 3, the radiant show “Desert Painters of Australia:Works from the Kluge-Ruhe Aboriginal Art Collection of the University of Virginia and the Collection of Steve Martin and Anne Stringfield” features 10 artists, mostly of the Pintupi people, whose understanding of time, land and value operates in productive tension with that of the global art world. And, through May 27, MoMA PS1 is presenting an ambitious exhibition by the Karrabing Film Collective, whose members, from the Belyuen community, dramatize the historical disinheritance of their land as well as the daily joys and humiliations of Indigenous life.