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.

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.

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.

At its best, theatre is great at putting resonant metaphors on stage. And, as Elinor Cook’s new play abundantly proves, the activity of mountain climbing seems very promising as a metaphor for masculine endeavor. All that effort, all that heaving, all that straining. Blood and sweat and sometimes tears. And then the question: why do men want to stand on top of the world? And is it just men who have this urgent need for power and dominion?

Very occasionally the playing of a play leaves a deeper impression than does the play itself. This is the case with Good Canary, a lippy, sweary tragicomedy by Zach Helm about secrets and addiction on the New York publishing scene. It has already played in translation in Mexico and in France, where it won Molière awards for direction and design. Its director, the prolific screen and stage actor John Malkovich, now brings it to London for the first time – and obligingly lends his famously dark-chocolate tones to the reminder to turn off mobile phones.

Michael Head's new play is based on the book They Took the Lead by Stephen Jenkins, which tells the true story of events at Clapton Orient (now Leyton Orient) Football Club during the First World War, when 41 men associated with the east London team – players, backroom staff and supporters – joined up en masse to fight the Kaiser. Three never returned and several others were seriously injured.