She is Montague Burton Chair in International Relations at the University of Oxford and holds a Professorial Fellowship at Balliol College.

[4] Crawford received her Bachelor of Arts from Brown University in 1985, where she pursued an independent concentration entitled "The War System and Alternatives to Militarism."

From 1994 to 1996, Crawford completed a post-doctoral fellowship at Brown's Watson Institute for International and Public Affairs.

The project is the most extensive and comprehensive public accounting of the cost of post-September 11th U.S. military operations compiled to date.

[7][8] Since October 2017, Crawford has served on the board of the nuclear non-proliferation advocacy organization, Council for a Livable World.