He is an Honours graduate from the Royal Academy of Dramatic Art where he won numerous awards including Best Actor and Most Promising Actor, and is now an Associate Member. He was a member of The National Theatre Company both at The Old Vic in Olivier’s company and on the South Bank for Peter Hall’s company. Among his productions were Danton's Death, A Woman Killed with Kindness, The Merchant of Venice (with Olivier), Long Days Journey into Night (again with Olivier), The School for Scandal , Richard II, The Front Page, and Macbeth. He was invited back to appear with them at Queen's Theatre in the West End in the Italian Comedy Saturday, Sunday, Monday directed by Franco Zeffirelli and Laurence Olivier where he won a Best Actor nomination in the Critics' Circle Theatre Award. Later he was invited to join The National again on the South Bank under Peter Hall in the revival Death of a Salesman directed by Michael Rudman with Warren Mitchell winning himself another Best Actor Nomination in the Olivier Awards. He was back again at the invitation of Nick Hytner to join his inaugural season appearing in "His Girl Friday", "Edmund" and the Xmas show "His Dark Materials" directed by Hytner. He was with Elaine Stritch in The Gingerbread Lady, Denholm Elliott in "The Paranormalist", Frank Langella in Abracadaver, Albert Finney in Ronald Harwood’s Reflected Glory, Felicity Kendal and Frances de la Tour in Fallen Angels, Joseph Fiennes in George Dillon and Lesley Manville in Six Degrees of Separation.
Greif has been in many films including Lasse Hallström’s Casanova, Shoot on Sight, Eichmann, Spartan, The Upside of Anger, Boogie Woogie and Fakers. His many TV appearances include Spooks, Mistresses, He Kills Coppers, Silent Witness and the last ever story of Waking the Dead.
He has recently reprised his role of Travis in two new audio stories of Blake's 7 for Big Finish Productions.