The Persians, Cilieni Village, Brecon Beacons<br/>Earthquakes in London, NT Cottesloe, London<br/>My Romantic History, Traverse, Edinburgh

It's not every day you find yourself wandering round a ghost village, on a Welsh hilltop, in pursuit of an ancient Greek tragedy.

Normally, civilians aren't allowed to set foot in Cilieni: a pretend settlement, purpose-built by the British Army on the Brecon Beacons military range, to train troops in fighting house-to-house.

Right now, however, it's the setting for Aeschylus's The Persians, National Theatre Wales' extraordinary al fresco staging of the world's oldest surviving play, which is also a military reportage (from 47BC). It vividly describes the Battle of Salamis, when the democracy of Athens outmanoeuvred the forces of Xerxes' mighty Persian empire, crucially shifting the balance of power.

Cilieni is spooky. Burnt-out tanks hulk under cherry trees. Concrete chalets, with steel-shuttered windows, are clustered round a church, which looks suspiciously like a watchtower. Mike Pearson's vaguely modern-dress production gets rolling as the chorus of Persian elders noses its way through the milling audience in a vintage Rover. They're grey-suited apparatchiks holding the fort while Xerxes is warmongering, dispensing propaganda through megaphones. In Kaite O'Reilly's new adaptation, they glorify their ruler's supposedly unvanquishable troops, underlining that "failure is not in our language".

But then we follow them to Xerxes' palace: a four-storey house with no front wall and a stunning backdrop of mountains under a darkening sky. We overhear the elders inside this HQ privately confessing to fears, joined by Sian Thomas's brittle Queen Atossa, who's plagued by ominous dreams.

Unfortunately, Pearson's excessive use of video becomes problematically distracting and doesn't make complete sense either. Patently, this is a surveillance-obsessed society. Yet Xerxes' deputies appear not to grasp that we're still watching them, Big Brother-style, though a roving cameraman has filmed us and is following them all over the palace. His footage is beamed on to a big screen at loft-level. One chorus-member also has a mini-camera on his wrist, whence lurching images are simultaneously relayed to TV monitors on every floor.

You might think that, when the news of Persia's terrible defeat reaches Attossa, Thomas's desolation would be more poignant for being cinematically magnified. Actually, though, the multimedia split focus leaves you less engaged. That said, the chorus's mute dance of grief – slowly crumpling across their conference table and rolling it over – strikingly reflects the account they're hearing of sinking ships and drowning men. Paul Rhys is also mesmerising as the ghost of Xerxes' father, his video appearance rendered eerie by freeze frames, and his howling face fading to a skull-pale blur.

This staging avoids any very specific references to on-going conflicts between the West and Middle East. But The Persians is a fascinating piece of work per se: clearly, in part, rejoicing in the Greeks' victory, yet written by a war veteran turned dramatist who chose to tell the story as a tragedy, seen through the eyes of the losing side.

In Earthquakes in London, we are faced with a battle for supremacy between the planet and mankind. Mike Bartlett's epic saga, premiered by the director Rupert Goold, is about three sisters and the civilised world in meltdown. The siblings' estranged father, a hard-line environmental guru called Robert (Bill Patterson), sees it as retribution: the natural world, sick of our pollution, responding with cataclysmic high temperatures and floods. Only extreme measures – slashing the population – can pull us back from the brink.

In flashbacks, we see the younger Robert as a scientific researcher, lured by honchos from an airline company. In present-day London, his eldest daughter, Lia Williams' Sarah, is the coalition government's radical new Environment minister. Her bolshy kid-sister Jasmine (Jessica Raine) has worked a rainforest theme into her burlesque strip routine. Meanwhile, Anna Madeley's Freya is pregnant and having a suicidal breakdown, drifting from Hampstead Heath to Waterloo Bridge, slipping en route into hallucinatory visions of the past and the future (with surely a nod to Angels in America).

Far from gloomy, Goold's production is exhilarating, with snazzy set design by Miriam Buether. The audience stand or sit on spinning bar stools, as Bartlett's characters cross paths – and go off the rails – on a walkway that snakes across the auditorium. The surrounding walls flow with images of city streets, and Goold overlaps scenes quite brilliantly, capturing the hectic speed of modern life and of imaginative leaps. The acting is excellent too, especially Tom Goodman-Hill as Williams' sidelined husband – desperately unhappy, then wildly pogoing.

You might expect more scientific grist. And the messianic turn Bartlett's storyline takes – accompanied by an animated cartoon – disappoints. Cavils aside, though, Earthquakes is a hot ticket: big, bold, imaginative and politically engaged.

D C Jackson is a name to watch. His outstanding new play, My Romantic History at the Edinburgh Fringe Festival is, for starters, a highly entertaining office comedy in which the narrating anti-hero, Iain Robertson's Tom, is a small-time feckless cad. Currently, he's trying to extract himself from a fling with a workmate, Amy (Alison O'Donnell), who thinks he's Mr Right. However appallingly he behaves, she won't chuck him.

The witty twist is that we then see all this replayed, slightly differently, from Amy's viewpoint, which is equally sardonic. And from there My Romantic History becomes an unexpectedly probing piece about self-delusion, maturing love and compromises. Lyndsey Turner's delightful production – playfully using office flipcharts and overhead projectors in the storytelling – is a delight. It tours to Birmingham, Sheffield and London's Bush Theatre.

'The Persians' (01874 611622) to 21 Aug; 'Earthquakes in London' (020-7452 3000) to 22 Sep; 'My Romantic History' (0131-228 1404) to 29 Aug, and touring

Next Week:

Kate follows the aimless drifters of Hemingway's The Sun also Rises, adapted for the stage