A Rhodes Scholar, Professor Edwards has held a Harkness Fellowship, based at Duke University in the United States, a Harold White Fellowship at the National Library; a Research Fellowship and a Visiting Fellowship at the Australian National University; a Visiting Scholarship at the John Curtin Prime Ministerial Library; a Visiting Professorship at the University of New South Wales, Canberra and a part-time professorship at Flinders University.

A recently published festschrift for the distinguished historian and strategic expert, Emeritus Professor Robert O’Neill, War, Strategy and  History: Essays in Honour of Professor Robert O’Neill (Daniel Marston and Tamara Leary (eds.), ANU Press, Canberra, 2016), includes a chapter by Peter on ‘Robert O’Neill and the Australian Official War Histories: Policy and Diplomacy’.