Expanding the Aboriginal and Torres Strait Islander Australian (hereafter respectfully Indigenous) talent pool to undertake valuable roles in business, health, education, academia, government, policy development and community development is critical for addressing current disparities between Indigenous and other Australians. Parity of access and engagement with education plays a key role in facilitating participation in these roles but has not yet been attained. This article provides "an initial" systematic review of literature on the state of the evidence regarding access/attraction, retention and completions for Indigenous Higher Degree Research (HDR) students. This article identifies the quantity (number examined), nature (e.g. focus of study), quality (peer reviewed and evidence of methodological rigour) and characteristics (e.g. publication type, authorship) of the limited publications. Using specific search strings (words or phrases of relevance to the topic), a systematic review methodology was employed to search nine databases and grey (non-peer reviewed) literature from 1995 to 2015. The resultant 12 publications were mined with quality assessed and a predetermined framework used to extract and synthesise the characteristics from individual publications. This research contributes to existing literature about Indigenous Peoples in HDR programs internationally in identifying significant cultural and institutional barriers and highlighting institutional enablers which can contribute to attraction, retention and completion. Building on the prior limited research reported in the review, the article highlights the need for further research and provides an initial agenda of directions for universities and government to redress the disparity in entry and completion of Indigenous Peoples in HDR programs.