Greg began his career with the RSC as an actor in the 1987-88 season, becoming an Assistant Director in 1989. He was made an Associate Director in 1996 and became Chief Associate Director in 2006. He is an Honorary Fellow of the Shakespeare Birthplace Trust, and an Honorary Senior Research Fellow of the Shakespeare Institute. He has been awarded Honorary Doctorates by the University of Huddersfield, the University of Nottingham, the University of Bristol, the University of Warwick, the University of Birmingham, the University of Hull and the University of York. He was also the 2012-13 incumbent of the Humanitas Visiting Professor in Drama at Oxford University.
In June 2021 Greg directed, alongside Owen Horsley, Henry VI Part One; Open Rehearsal Project, which invited audiences inside the full rehearsal process for the first time in the company’s history.
In November 2019, Greg opened The Boy in the Dress – a new musical of David Walliams’ heart-warming comedy telling the story of star striker and fashion lover Dennis, adapted by former RSC writer-in-residence Mark Ravenhill, with new songs from Robbie Williams and Guy Chambers.
Greg’s production of Measure for Measure opened in the Royal Shakespeare Theatre in July 2019 and transferred to the Barbican in November that year
At the end of 2018 Greg directed Troilus and Cressida, collaborating with virtuoso percussionist Dame Evelyn Glennie to create a futuristic vision of a world echoing with the rhythm of battle. The production marked the first time the RSC explored a full-length Shakespeare play with a cast with an equally gender-balanced cast.
In 2017 Greg directed Imperium Part I: Conspirator and Imperium Part II: Dictator. Based on the Cicero Trilogy by Robert Harris and adapted by Mike Poulton, the six plays played over two performances, with Richard McCabe returning to the company in the role of Cicero. In the same year, in association with Little Angel Theatre Company, he also revived his celebrated production of Shakespeare’s epic poem Venus and Adonis.
On 23 April 2016, to mark Shakespeare’s birthday and the 400th anniversary of his death, Greg directed Shakespeare Live! From the RSC. In a unique collaboration with the BBC, hosted by David Tennant and Catherine Tate, this special event celebrated Shakespeare’s legacy across the performing arts. In the same year, he directed King Lear with Antony Sher in the title role, in the Royal Shakespeare Theatre, the Barbican and two years later at Brooklyn Academy of Music. he also directed The Tempest, with Simon Russell Beale returning to the RSC as Prospero. In collaboration with Intel and in association with Imaginarium Studios, the production conjured Prospero’s magical island in an innovative new staging.
Greg directed Henry V in autumn 2015 on the 600th anniversary of the Battle of Agincourt, before reviving his productions of Richard II and Henry IV Parts I & II, and all four plays performed together for the very first time at the Barbican Theatre under the banner King and Country from November 2015 until January 2016, launching the RSC’s celebrations of the 400th anniversary year of Shakespeare’s death. The productions then embarked upon a tour to Beijing, Shanghai and Hong Kong in February and March 2016 - the first time the RSC has taken the work from its main repertoire to the People’s Republic - before finally arriving at the Brooklyn Academy of Music in New York.
In 2015, the centenary year of Arthur Miller’s birth, Greg directed Death of a Salesman, with Antony Sher as Willy Loman, Harriet Walter as Linda Loman, and Alex Hassell as their son, Biff.
In 2014, Greg directed Henry IV Parts I & II with Antony Sher as Falstaff, Jasper Britton as Henry IV, and Alex Hassell as Hal, and The Witch of Edmonton in the Swan Theatre with Eileen Atkins.
In October 2013 Greg reunited with David Tennant, directing Richard II in the Royal Shakespeare Theatre then the Barbican. It became the first RSC Shakespeare production to play live to cinemas around the world in November.
Other RSC productions include: Julius Caesar, The Orphan of Zhao, Written on the Heart by David Edgar, Cardenio, Morte d'Arthur in an adaptation by Mike Poulton, Twelfth Night, Hamlet [with David Tennant in the title role, Patrick Stewart as Claudius, and winner of The Whatsonstage Best Regional Production and Theatre Event of the Year in 2009], A Midsummer Night's Dream and Love's Labour's Lost, Macbeth, Antony and Cleopatra, Coriolanus, All's Well That Ends Well, The Taming of the Shrew (paired with John Fletcher’s The Tamer Tamed), Much Ado About Nothing, The Winter's Tale, Othello, Merry Wives The Musical, The Merchant of Venice, As You Like It, King John, Timon of Athens, All Is True (Henry VIII), Venus and Adonis (in collaboration with The Little Angel Theatre), Rostand's Cyrano de Bergerac, Oroonoko by Biyi Bandele (after Aphra Behn), The Odyssey adapted by Derek Walcott, Jubilee by Peter Barnes, and co-directed a Mike Poulton adaptation of The Canterbury Tales.
In 2002, Greg led a season of five seldom-performed Jacobean and Elizabethan plays and directed The Island Princess by John Fletcher at the Swan Theatre and Gielgud Theatre, and received an Olivier Award for Outstanding Achievement of the Year.
Production elsewhere include: Anjin: The Shogun and The English Samurai by Mike Poulton and Shochiro Kawaii (Tokyo 2009 and 2012, Sadlers Wells 2013), The Merchant of Venice (Tokyo 2007), York Millennium Mystery Plays (York Minster), Black Comedy and The Real Inspector Hound (Donmar Warehouse Productions – Comedy Theatre), The Giant by Antony Sher (Hampstead Theatre), Mahler's Conversion by Ronald Harwood (Aldwych Theatre), Titus Andronicus (Market Theatre, Johannesburg and RNT Studio – TMA Award for Best Production), Twelfth Night, Ulysses (in Dermot Bolger's adaptation, Philadelphia), A Midsummer Night's Dream (NY State University), The Joker of Seville (Walcott/McDermott musical, Boston/Trinidad), Edward Bond's September (Canterbury Cathedral), Frank McGuinness’ Someone to Watch Over Me (Theatr Clwyd), Two Dogs and Freedom (Sadlers Wells and Channel 4). As Artistic Director of Century Theatre: The Importance of Being Earnest, Bedroom Farce, An Inspector Calls, Private Lives. As Associate Director of Nottingham Playhouse: Long Day's Journey Into Night, Waiting For Godot, The Norman Conquests, Hester, The Rose and The Ring.
His filmed version of Hamlet (BBC2/Illuminations) was broadcast in the UK on Boxing Day 2009 and in the US on PBS. His other film work includes: Macbeth (Channel 4 / Illuminations) and A Midsummer Night's Dreaming (BBC4 documentary based on research for his own production); and he directed extracts from various Shakespeare plays for Michael Wood's BBC series, 'In Search of Shakespeare'. Illuminations also filmed his World Shakespeare Festival production of Julius Caesar, which was broadcast on BBC4 as part of the BBC's Shakespeare season for the Cultural Olympiad in June 2012.
With the British Library, Greg compiled two CDs of extracts from live recordings of great performances from Stratford since the late fifties: Essential Shakespeare LIVE!, and Essential Shakespeare ENCORE!
Writing credits include Woza Shakespeare! co-authored with his partner Antony Sher about their production of Titus Andronicus in South Africa in 1995; The Shakespeare Almanac in 2009; and Shakespeare's Lost Play: In search of Cardenio in 2011.
On 13 February 2017 Greg gave the sixth Annual London Shakespeare Lecture in honour of Sir Stanley Wells at the University of Notre Dame. In June 2012 he received the Sam Wanamaker Award from Shakespeare's Globe Theatre, an annual award that recognises and celebrates work which has increased the understanding and enjoyment of Shakespeare.
Greg delivered the 2016 Richard Dimbleby Lecture, which was broadcast on 16 March 2016 to coincide with the 400th anniversary of Shakespeare’s death.