Rhys spent the first decade of his career as an academic at La Trobe University, researching parallel and distributed computing systems. There followed a decade and a half in research programme management leading to strategic management roles in Australia’s Commonwealth Scientific and Industrial Research Organisation. His appointments included becoming the organisation's first coordinator for its overall research in information and communication technologies and its first director for high performance scientific computing. During this period Rhys also programme managed the national grid implementation for the Australian Partnership for Advanced Computing. 

In 2006 Rhys accepted an opportunity to support the Australian Government’s National Collaborative Research Infrastructure Strategy by facilitating the development of a national plan for investment in eResearch. He was subsequently appointed as the Executive Director of the Australian eResearch Infrastructure Council to guide the implementation of that plan. The Council concluded its function in 2013 and Rhys now directs an eResearch Coordination Project aiming to further assist the national eResearch development projects and infrastructure operators, to work towards improved data supply and data using services in support of Australian research communities.