Legacy of an 'American great'
Playwright David Hare said on Friday that Miller completed a triumvirate of writers who redefined the parameters of the American stage.
"Arthur was the last of the three great theatrical voices of the American century - (Eugene) O'Neill, (Tennessee) Williams, Miller," he said.
"Arthur's special achievement was to make political and social plays which belonged on Broadway and yet were also powered to reach out into America and way beyond."
Nicholas Hytner, director of the Royal National Theatre, was quick to echo Hare's sentiments.
"He brought to the English-speaking theatre a poetic urgency and tragic sweep that had been absent since the Elizabethan era," he said.
"I have no doubt that plays like Death Of A Salesman, The Crucible and A View from the Bridge will always stand with the masterpieces of Ibsen, Shakespeare and Sophocles."
Hytner, who directed the 1996 film version of The Crucible, said "the uncompromising morality of his world view", particularly in his later years, meant he was better appreciated outside his home country.
"America felt rebuked by him. Many Americans have felt insulted... his refusal to meet them halfway was the magnificent stubbornness of the great artist."
Alan Yentob described Miller as "a towering figure, both physically and intellectually".
The producer, who recently made a profile of the playwright for his Imagine TV series, said he remained "politically engaged to the very end".
All My Sons and The Price have recently enjoyed successful revivals in London's West End, with a new production of Salesman opening in May.
"Those plays are enough to mark him out as one of the greatest playwrights ever," said Mark Shenton of the Sunday Express.
"But actually the whole body of his work is unrivalled.
"He wrote all the way through his life, right to the end," Shenton continues.
"To be working at 89 is phenomenal, but to still have something to say is even more so."
Tapped into zeitgeist
Miller's ability to tap into the American zeitgeist, most notably in the post-war years and the McCarthy era, made him as much a social and cultural commentator as a dramatist.
And his unlikely marriage to Marilyn Monroe briefly transformed him into a reluctant pop-culture icon.
"His plays expressed the range of human experience and his incredible capacity to identify with people," said Mr Thacker.
"That's why he was such an important playwright for our time. He showed us what was possible about being a human being."
Miller's pre-eminence was signalled early on his career when he won three Tony Awards in the first seven years of their existence.
"That's an extraordinary recognition for a playwright who was really just emerging on the scene," said Howard Sherman of the American Theatre Wing, the body that established the Tonys in 1947.
"He was a contemporary of Tennessee Williams, who was also writing at this time, and quickly leapt into the pantheon of great American writers.
"There is no question that Arthur Miller's effect on American drama and drama worldwide is something we're going to be recognising for centuries to come."