The perception of Steven many-hats Berkoff as “one of the major minor contemporary dramatists in Britain” makes sense when you see this. Here are two chamber pieces, both two-handers, written 20 years apart, which gain hugely from being run together. Indeed, it’s hard to imagine either of them having much of a life as a single entity, since even combined they make a short evening at the theatre.

To begin writing a book is to start something over which you are going to lose control. As it comes to life, a book acquires its own quiddity, its own interior authority, and if the writer does not obey this authority she ruins the book. A Man of Good Hope tells the true story of Asad, a Somali refugee who embarks on an transcontinential journey to reach South Africa. About halfway through the writing, the book began demanding that I stick uncompromisingly to Asad's point of view as he was subjected to South Africa’s relentless, slow-drip violence.

Ye olde love triangle returns, this time as the centrepiece of a rock chamber musical that premiered Off-Broadway in 2013 and now makes its UK premiere. There’s a good guy, a bad boy, and the promise of a violent end, but despite the oft-referenced roiling passions – and a storming quartet of performances – Sam Yates’s staging feels too cool and clinical for its purportedly hot-blooded subject.

Fleeing rape and forced marriage in their war-torn homeland, a boatload of women refugees washes up in Greece, where they beg asylum from the suspicious locals. No, not a depressingly familiar news story of our own times, but the basis of Aeschylus’s 2,500-year-old drama The Suppliant Women – an ancient work whose unmistakable contemporary resonances David Greig brings unashamedly to the fore in his brand new adaptation.

Is this the most dazzling play of a dazzling playwright? First staged in 1974, Travesties is the one which manages to squeeze avant-garde novelist James Joyce, Dada godfather Tristan Tzara and communist revolutionary Lenin into a story which resembles a riotous party, where Wildean pastiche, political history, debate about art, unreliable memory and song-and-dance routines stay up half the night, and howl gloriously at the moon.

Nobody said that a 70-minute audience with the undead was going to be easy. You can read Samuel Beckett's Texts for Nothing in your own time, pausing for thought, leaving off, coming back. When as compelling an actor as Lisa Dwan chooses not just to read it but to perform a selection for the first time, there's nowhere to hide – either for us or for her.

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.

It's one of those true stories you couldn't make up: in 1920s Kentucky, Floyd Collins, visionary cave explorer, happens across the spectacular sand cave of his dreams only to become trapped on the way back to the surface. The media attention he might have hoped would turn his discovery into a commercial proposition for him and his impoverished family is instead – irony of ironies –  focused on his entrapment.

Restoration theatre has the reputation of being a rake’s paradise – all those randy young aristos in hot pursuit of buxom wenches. But even in the depths of 17th-century playwriting, there was room for repentance and regret among the discarded petticoats and ripped bodices. So it is with Stephen Jeffreys’s The Libertine, his now sharply rewritten 1994 play that was also made into a film starring Johnny Depp.

What's in a name? Imogen has a softer music to it than Cymbeline, the only one of Shakespeare's plays in which the title character is marginal, and the daughter certainly dominates in a way that her regal father doesn't. So Cymbeline Renamed, as half the subheading of Matthew Dunster's bold production puts it, is fine.