[1] After university, in 1993 he co-founded a drama collective with fellow students Graham Eatough and Nick Powell called Suspect Culture, based in Glasgow.
When the National Theatre of Scotland was formed in 2006, Greig served as its first Dramaturg[5] and also wrote an adaptation of Euripides' The Bacchae for them.
His adaptation of Alasdair Gray's novel Lanark opened at the Lyceum Theatre as part of the Edinburgh International Festival in 2015.
He has produced adaptations of Tintin in Tibet (2005) for the Barbican, London, and Charlie and the Chocolate Factory (2013) for the Theatre Royal, Drury Lane.
The Strange Undoing of Prudencia Hart (2011) for the National Theatre of Scotland was designed to be toured to and performed in pubs; partnering with Punchdrunk, it played an extended run from November 2016 to April 2017 at the Heath restaurant in the McKittrick Hotel, home of the similarly immersive theatrical experience Sleep No More in New York City.
[7] With local politician Sarah Beattie-Smith of the Scottish Green Party, Greig curated the political discussion show Two Minute Manifesto which toured Scotland in 2015.
[12] The 2019 opening of Greig's first original new play in six years, Adventures With The Painted People, at the Pitlochry Festival Theatre was cancelled due to the COVID-19 pandemic.