Is Katori Hall (b. 1981) the embodiment of Martin Luther King’s dream? She was born in Memphis, the city where King died. The Mountaintop, her play about his last night alive, had its world premiere at Theatre 503, a tiny pub stage in south London. But the unanimity of the reviews, combined with the timely arrival of a black man in the White House, propelled the two-hander into the West End where it played to standing ovations from notably multiracial audiences.

She gave us the most moving King Lear years before the news broke that Glenda Jackson would be playing the role. Only Mark Rylance has recently matched the malicious wit of her Globe Richard III. Now Kathryn Hunter spellbinds in a very Shakespearean downfall drama about the court of Ethiopian Emperor Haile Selassie – but this time the Elect of God doesn’t actually appear in person, not literally at any rate, and the triumph is shared by everybody involved, lighting and soundscape designers included.

Billie Piper vaults to the top rank of British theatre actresses with Yerma, Australian writer-director Simon Stone's rabidly free rewrite of Lorca's 1934 play that posits its young star as the sort of take-no-prisoners talent whose gifts come not from drama school but from something gloriously unfettered and astonishingly free.

Joe Penhall’s Blue/Orange is one of the best plays of the past two decades. First staged at the National Theatre in 2000, with the dream cast of Chiwetel Ejiofor, Andrew Lincoln and Bill Nighy, it won an Olivier Award for Best Play and has been constantly revived ever since. Not only does it have a strong story, but the characters, and their interaction, are credible, engaging and dramatic, while the play fizzes with ideas as well as emotions. It is a contemporary classic.

Joe Penhall first thwacked his way to the attention of British theatregoers more than 20 years ago with a series of plays about schizos and psychos and wackos. An iconoclastic laureate of lithium, his early hit Some Voices (1994), about a care-in-the-community schizophrenic, went on to be filmed starring Daniel Craig. In 2000 he returned to the subject in Blue/Orange.

It’s easier to say what Jane Horrocks’s new musical dance-drama isn’t that what it is. Horrocks makes a short speech at the beginning and the end about the mysteries of love, as depicted in her selection of Mancunian heartbreakers from Gang of Four, Joy Division, Buzzcocks and The Smiths, among others. But there’s no narrative, as such, or individual characters, and the songs are only connected with a series of semi-abstract dance routines usually performed at the front of the stage, and often involving Horrocks herself.

Legendary director Peter Brook makes theatre that teaches audiences to be human. Now 90 years old, he brings his latest project to London from Paris, where he has been based at the Bouffes du Nord since quitting the UK more than 40 years ago. Called Battlefield, it is a 65-minute distillation of part of his 1985 11-hour epic, The Mahabharata, and revisits the ancient Sanskrit myth of the Kurukshetra War, and the struggle between the two warring families of the Kauravas and the Pandavas.

Events have overtaken this Macbeth, dramatically heightening its queasy topicality. Not just brutal beheadings and torture, but the cost and collateral damage of conflict without end, and the scourge of a tyrant slaughtering his own people, strike one anew in the wake of recent debate. Carrie Cracknell’s interpretative, modern-dress production traps us in a military underground bunker, drained of light and colour – a Hell as acutely psychological as it is physical. Not for nothing does the doomed Macbeth fear the “diseased mind”.

This year’s Olivier Awards saw the Young Vic trounce its South Bank neighbours, with Ivo van Hove’s revolutionary A View from the Bridge leading 11 nominations and four wins; the production opens on Broadway next week. It reflects an extraordinary period during which the theatre, originally an offshoot of the National, has grown to become one of Britain’s major creative powerhouses – all under the aegis of South African-born David Lan, artistic director since 2000.

“My brother died.” That’s the reality New York-based banker Willem struggles to inhabit when he returns to his estranged family in Amsterdam. There is no sense in Pauli’s loss – a sudden heart attack at 20, cradled by a stranger in the street – nor finality. Willem’s response is to continue the conversation through an elegiac series of letters, countering the abandonment and searching for meaning in both a life interrupted and his own isolated existence.