Remembered for his scholarship in the fields of Islamic and Near and Far-Eastern studies, Muir is also known for serving as an imperial administrator and governor in Bengal and British India. His best-known publications include The Koran: Its Composition and Teaching; Annals of the Early Caliphate; and A Life of Mahomet.
After studying at the Universities of Edinburgh and Glasgow, he became a civil servant in Bengal.
One of his early works, Life of Mahomet, was controversial for its criticism of Islam.
He grew up in Glasgow, Scotland, with a brother named John. His marriage to Elizabeth Huntly Wemyss resulted in eleven children, including a son, Colonel A. M. Muir, who was also involved in Far Eastern politics.
American author Daniel Pipes traced the use of the controversial phrase "Satanic Verses" to one of Muir's scholarly works.