The Tempest, King's Theatre, Edinburgh<br/>King Lear, Royal Lyceum, Edinburgh<br/>Top Girls, Trafalgar Studios, London

A Seoul theatre company beautifully peoples Prospero's island with swirling dancers, but a Chinese attempt to double up Lear and his Fool is a muddle in Mandarin

Prospero was king of the castle once, before his usurper brother cast him adrift on the ocean.

Now he is seeking vengeance. At the start of The Tempest "after William Shakespeare" – beautifully envisaged by Seoul's Mokwha Repertory Company at the Edinburgh International Festival – Prospero's old enemies are being shipwrecked in a whirl of spume-white shawls. To frantic drumming, they dance their drowning moments on a bare, misty stage. They spin in traditional, wide-skirted robes and keel over, to tumble like corpses in a rip tide. Some, as if dreaming an afterlife, wake on the remote isle where Prospero now holds sway.

In this free adaptation by director Tae-Suk Oh, which mixes the Bard's late romance with old Korean tales and folk songs, Prospero (aka Zilzi) is a storm-conjuring shaman with a cloud of dark hair. He is also traumatised and hysterical, like a child in a violent tantrum, when he recalls his past ill-treatment. That is echoed later, when he makes Alonso, his brother's ally, suffer the pangs of bereavement, by conjuring up a hallucinatory masque. Beholding his son, Ferdinand, dead and borne away by pig-headed demons, Alonso falls into a juddering fit: a turning point after which Prospero moves from retribution towards reconciliation (and more self-reproach than in Shakespeare).

Perhaps Caliban is supposed to be a hopeful allegory for North and South Korea too. This comic monster, with two quarrelling heads, is finally sawn in half, leaving both twins – though the op looks momentarily lethal – to skip away, chorusing "Freedom!" At times, this production is crowd-pleasingly cute and Oh's script doesn't improve on Shakespeare either, with its bowdlerised titbits from the original (or so the English surtitles suggest). Yet it can be delightfully cheeky. Castaways merrily chat to the goats and monkeys in gobbledygook. Prospero's daughter Miranda is a sweet-natured child with a smiling, full-moon face. And presenting The Tempest as a folk play – staged with sophisticated minimalism – is certainly winning.

The EIF's director, Jonathan Mills, has enthusiastically imported a cluster of Asian productions this year. I struggled with King Lear, nonetheless, reconceived as a one-man show and performed in Mandarin by Wu Hsing-kuo of China's Contemporary Legend Theatre (with more Shakespeare snippets). Maybe Peking Opera just isn't my cup of tea. For sure, Hsing-kuo's Lear looks spectacular, playing the grief-maddened king spotlit in a stone circle of gigantic statues. His armoured robes are like silver dragon's scales, his painted face a rancour-furrowed mask, framed by a dandelion clock of white hair and beard.

Although it's vintage music theatre, Peking Opera can also sound electrifyingly avant-garde to an untrained Western ear, with raucous ululations, wooden clappers and piping akin to a whistling kettle. I have to confess I did find that increasingly wearing, and over-amplified. It's also hard not to liken puzzling elements to your own cultural frames of reference, in a possibly hardwired impulse to understand that can, nonetheless, generate a sense of inappropriate absurdity.

Stomping around in platform-soled tragic buskins, this Lear looks regrettably like a Gary Glitter comeback. And in act two, when Hsing-kuo starts switching roles, his Fool's waddling and stunts aren't very entertaining. Perhaps there's a whiff of limelight-hogging megalomania about the self-directed, solo format, even if "Delegate more" is hardly the moral of Lear's tale. Hsing-kuo's places one foot in modernity, stepping out of Shakespeare's story to express an actor's angst about his own artistic struggles. He keens with a musical intensity that, if self-absorbed, is touching.

Men don't even get a look-in when it comes to Caryl Churchill's 1982 classic Top Girls – transferring to London from Chichester Festival. The shoulder-padded, steely Marlene (Suranne Jones) is taking charge of an employment agency in the City. The office chairs are all, pointedly, upholstered in Thatcher blue in Max Stafford-Clark's excellent revival. Back in the sticks, Stella Gonet's frustrated Joyce is bringing up Marlene's abandoned and slightly backward daughter, Olivia Poulet's Angie. Meanwhile, in a more surreal vein, Marlene has managed to organise a dinner party with admired women from past ages as her VIP guests. These include the legendary transvestite Pope Joan (a dryly amusing Lucy Briers); a Victorian lady-traveller (Gonet, again); Brueghel's devil-routing Dull Gret (Poulet), and Chaucer's Patient Griselda (Laura Elphinstone).

Marlene's lip curls superciliously at passé role models who kowtowed to patriarchal bullying, but isn't that Seventies feminism already going askew? Churchill and Stafford-Clark's cast sharply highlight how sisters who've had to struggle for independence and empowerment can be aggressive, egocentric and conversationally override each other. That said, careful naturalistic detailing draws out suppresses veins of tenderness.

Churchill's scene-structuring feels, still, radically experimental: jagged and slanted; the theatrical equivalent of Daniel Libeskind's architecture. Moreover, way beyond the issue of gender, this play's sociopolitical worries – about flashy top dogs and a disgruntled underclass who could turn nasty – are far from outdated.

Top Girls' (0844 871 7632) to 29 Oct

Next Week:

Kate Bassett settles down for Tim Supple's One Thousand and One Nights

Theatre Choice

At the Edinburgh Fringe Festival, Thirsty is Paper Birds' vivacious and worrying portrait of booze-sodden Brits, blending anecdotes and dance (Pleasance, to 28 Aug). Simon Callow is sweetly touching as a long-suffering transvestite in Tuesday at Tescos, though the final dark twist is abrupt (Assembly Hall, to 29 Aug).