Murray is Scottish History Adviser and a board member of the National Trust for Scotland and holds the Bradley Chair of English Literature at the University of Glasgow. He is a former Chatterton Lecturer at the British Academy and BP Humanities prizewinner of the Royal Society of Edinburgh of which he is a Fellow. Murray is a regular broadcaster, including a number of Jacobite-related programmes for In Our Time.
His research includes groundbreaking books on Jacobite armies, literature and material culture, on national cultures, the construction of Celtic identities and the existence and nature of a distinctive Scottish Romanticism. He is currently working on a history of the British Army in Scotland after 1746 and The Global History of Scotland.