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Previously he held chairs at the Imperial College of Science, Technology and Medicine, and at the University of Edinburgh.
He holds MA degrees from Cambridge and Oxford, and a PhD from the University of London.
He is a Fellow of the Royal Society (2004), a Fellow of the Royal Society of Edinburgh (2000), a Member of Academia Europaea(1993), and a Fellow of the ACM (2014).

His paper “Domain theory in Logical Form” won the LiCS Test-of-Time award (a 20-year retrospective) for 1987. The award was presented at LiCS 2007.
His paper “A Fully Abstract Game Semantics for General References” with Kohei Honda and Guy McCusker won the LiCS Test-of-Time award (a 20-year retrospective) for 1998. The award was presented at LiCS 2018.
He was the Clifford Lecturer at Tulane University in 2008.
He was awarded the BCS Lovelace Medal in 2013.
He received the Alonzo Church Award for Outstanding Contributions to Logic and Computation in 2017.

He has played a leading role in the development of game semantics, and its applications to the semantics of programming languages. Other notable contributions include his work on domain theory in logical form, the lazy lambda calculus, strictness analysis, concurrency theory, interaction categories, and geometry of interaction. More recently, he has been working on high-level methods for quantum computation and information. He introduced categorical quantum mechanics with Bob Coecke. He introduced the sheaf-theoretic approach to contextuality and non-locality with Adam Brandenburger, and has contributed extensively to developing a structural theory of contextuality and its applications.

Current work is focussing on contextuality as a resource for quantum advantage. Topics include quantifying contextuality and a resource theory for contextuality, and connections with non-local games giving rise to a quantum monad on relational structures. This is ongoing work, with a number of collaborators past and present including Adam Brandenburger, Lucien Hardy, Shane Mansfield, Rui Soares Barbosa, Ray Lal, Phokion Kolaitis, Georg Gottlob, Kohei Kishida, Nadish de Silva, and Giovanni Caru.