Two countries; two histories. Being black in the US; being black in the UK. Compare and contrast. Which is exactly what debbie tucker green’s amazingly ambitious new epic, which straddles centuries and continents, succeeds in doing. Taking a forensic look at what it means to be at the sharp end when you are Black British or African American, the show has a thrillingly unexpected theatre form and is written in green’s distinctive style of reiterative and repetitive punchy dialogues, which here are both emotionally passionate and imaginatively modernistic.

The Royal Court Theatre has long been a leader in new British drama writing. Thanks to Elyse Dodgson, who has died aged 73, it has built up an international programme like few others in the arts, anywhere. At the theatre, Elyse headed up readings, workshops (in London and abroad), exchanges and writers’ residencies that might have suggested a team of 15 or so but her department was modest in size.

There was once a time when grime music was very angry, and very threatening, but that seems a long time ago now. Today, Dizzee Rascal is less a herald of riot and revolt, and more of a national treasure, exuding charm from every pore, even if his music has become increasing predictable and safe. But, as wordsmith and dancer Debris Stevenson proves in her debut play, Poet in da Corner, Dizzee Rascal still can change minds and influence people.

Blackout. Dark, the colour of childhood fear. Black, the colour of despair. Black. No light visible; no colours to see. Just pitch black, maybe even bible black. This is how Robert Alan Evans’s The Woods, which stars the brilliant Lesley Sharp and which opened tonight in the Royal Court’s theatre upstairs, begins – in total darkness. Followed by images of desolation, the sound of torrential rain, the devastation of a falling tree. In the crepuscular gloom, the story begins to unfold.

The apocalypse arrives as a series of collegiate sketches in the aptly-named Pity, the Rory Mullarkey play that may well prompt sympathy for audiences who unwittingly find themselves in attendance.

It’s the stuff of nightmares. There’s a massive explosion, the sound of smashing glass, falling debris and police sirens. Gunshots. Panic in the streets. It could be the November 2015 Paris terror attacks, in which the Bataclan venue was the scene of a massacre, except this time it’s happening in London. Yes, the stuff of nightmares. And it is also the powerful start of Cordelia Lynn’s new play, One for Sorrow, which has just opened at the Royal Court's upstairs studio space.

Anna Deavere Smith contains multitudes. As the solo performance artist recounts the testimonies she has selected from the more than 250 people she interviewed for this portrait of inequality and the criminal justice system in America, it is as if each person she has talked to possesses her.

Playwright Anthony Neilson has always been fascinated by sex. I mean, who isn’t? But he has made it a central part of his career. In his bad-boy in-yer-face phase, from the early 1990s to about the mid-2000s, he pioneered a type of theatre that talked explicitly about sex and sexuality.

There’s a whole universe which British theatre has yet to explore properly – it’s called the sci-fi imagination. Although this place is familiar from countless films and television series, it is more or less a stranger to our stages.

In the same week that saw the arrival of Arinzé Kene’s Misty, a play that passionately questions the clichés of plays about black Britons (you know, gun crime, knife crime and domestic abuse), Black Men Walking opens at the Royal Court.