With this paper, we initiate the Supplement on Deepening our Understanding of Quality in Australia (DUQuA). DUQuA is an at-scale, cross-sectional research programme examining the quality activities in 32 large hospitals across Australia. It is based on, with suitable modifications and extensions, the Deepening our Understanding of Quality improvement in Europe (DUQuE) research programme, also published as a Supplement in this Journal, in 2014. First, we briefly discuss key data about Australia, the health of its population and its health system. Then, to provide context for the work, we discuss previous activities on the quality of care and improvement leading up to the DUQuA studies. Next, we present a selection of key interventional studies and policy and institutional initiatives to date. Finally, we conclude by outlining, in brief, the aims and scope of the articles that follow in the Supplement. This first article acts as a framing vehicle for the DUQuA studies as a whole. Aggregated, the series of papers collectively attempts an answer to the questions: what is the relationship between quality strategies, both hospital-wide and at department level? and what are the relationships between the way care is organised, and the actual quality of care as delivered? Papers in the Supplement deal with a multiplicity of issues including: how the DUQuA investigators made progress over time, what the results mean in context, the scales designed or modified along the way for measuring the quality of care, methodological considerations and provision of lessons learnt for the benefit of future researchers.