Professor Craig is Professor in English Law at the University of Oxford, who researches and writes on comparative public law, constitutional and administrative law, and European Union law.

He is the alternate UK member on the Venice Commission for Law and Democracy, which advises the Council of Europe on constitutional matters. He was made an Honorary QC in 2000, and an Honorary Bencher of Gray's Inn in the same year.

Professor Craig has lectured at many institutions across the world, including in North America, Europe, China and Australia. He is editor of the Clarendon Law series, co-editor of a monograph series on EU law in Context, and is on the editorial board of various law journals. He is also a delegate of Oxford University Press.