This paper comprises three big picture essays reflecting on Australian Indigenous policy of the last half century. The first two were originally written in 2018 as contributions to a major international gathering of political scientists. The third was written in early 2021 as a response to Westbury and Dillon’s initial 2019 contribution to the Centre for Aboriginal Economic Policy Research’s (CAEPR’s) 30th anniversary Policy Insights: Special Series. Section I, the first essay, grapples with ideas of structure in Indigenous policy, what endures and what changes. Five deep and persisting structures are identified and discussed: federalism, competing principles, high moralism, a remote focus, and the individual–communal dimension. Section II, the second essay, grapples with the idea of what a decolonising approach to Australian Indigenous policy might look like and how one might be brought about. Building on Rowse’s 2012 analysis of two idioms of social justice and recognition – ‘peoples’ and ‘populations’ – in Indigenous policy, it argues that the ‘peoples’ idiom must come to the fore. The final essay is longer and more complex, responding explicitly to Westbury and Dillon (2019). It summarises their two main arguments about political settlements and ongoing exclusion in order to develop points of debate. In so doing, it returns to and extends the discussion of three of the deep structures outlined in Section I: federalism, high moralism and a remote focus. This essay also connects the decolonising of Indigenous policy to the idea of deeply informed agency.