Over the last decade, there has been a steady increase in the number of Indigenous graduate research students in Australia, yet research and pedagogy has not kept pace with changes underway in the sector. From an extensive search of literature published between 2000 and 2017, 15 papers (representing 10 research projects conducted by seven teams or authors) were identified that addressed Indigenous graduate research student experience. Overall, the literature tends to focus on identifying barriers to completion, noting in particular the impact of financial difficulties, social isolation and racism. A research degree is a key site for the assertion and legitimation of Indigenous knowledges, and it is here that Indigenous students are navigating tensions between legitimated disciplinary practices of the centre and the peripheral status of Indigenous knowledges. We, therefore, adopt Herbert's 'centre-periphery' model to interpret the research, arguing that this framework explains the focus on barriers, the neglect of pedagogy centred on academic excellence and student strengths, and research relationships between students and Indigenous communities. Our review identifies the need for a systematic research agenda specifically focused on Indigenous student success at the graduate research level, and looking internationally in order to assess the performance and strategies of Australian higher education providers in comparison to international institutions meeting the aims of First Nations research communities. This approach, we suggest, should move beyond an analysis of the nature of enablers and barriers to focus on Indigenous Higher Degree by Research success.