Frozen, NT Cottesloe, London<br></br>The Island Princess, RSC Swan, Stratford-Upon-Avon, Blood Links, Barbican Pit, London

Paedophilia is not something we, the British, like talking about. Unless it's in the context of lynch mobs and throwing away the key. So Bryony Lavery's 1998 play, Frozen, about a man who has sexually abused and murdered seven children – revived by Bill Alexander for the National – is a brave and vital attempt to tackle the subject at both an intellectual and emotional level. Such is the discomfort surrounding the topic that Lavery's brilliant black humour frequently fails to raise a single titter, as if laughing would be construed as condonation or perversity. You can feel the audience collectively stiffen as Ralph (Tom Georgeson on magnetic form) surveys his suitcase of child porn videos, lovingly reading out the absurd and disturbing titles, like a little boy obsessively inspecting his collection of toys.

So we're presented with the monster, and like Nancy (Anita Dobson), the mother of one of his victims, we have to deal with the reality of him. Should he be killed? Can he be forgiven? Nancy's journey from paralysing shock to grief-stricken anger and, finally, a state of stoic acceptance, is a fascinating examination of the human spirit battling to overcome almost incomprehensible pain. But Lavery also dares to show the suffering of the man who has inflicted this agony. Josie Lawrence's criminal psychologist puts a very convincing case that Ralph's deviant behaviour is "a crime of illness", not evil, and that the psychological damage from years of child abuse is so profound that it has mis-wired his brain.

Contentious issues aside, this is also a cathartic study of grief, revenge and forgiveness (with Dobson impressively scaling all these emotions), of psychological distress and how it manifests itself physically (Ralph thinks he's got cancer because his body is racked with pain, the result, Lavery implies, of his body agonisingly thawing as the first pangs of empathy belatedly set in).

Lavery's monologues can be over-explanatory at times and the psychologist's back-story never quite finds its place in the narrative, but this is compelling theatre nonetheless (thanks, in no small part, to Alexander's measured direction and Paul Pyant's stunning lighting), a powerful example of drama treading where heated debate simply couldn't reach.

At the Swan in Stratford, the RSC's season of Jacobean rarities continues with John Fletcher's The Island Princess – a play which hasn't seen the light of day since the end of the 17th century. Considering its unpopularity, it's a surprisingly sprightly little number, a mostly light-hearted romp about the eponymous princess and her various suitors which touches on issues of colonial rule, racism and religious intolerance – but not at the expense of Fletcher's swashbuckling plot. The story owes something to The Tempest, with its exotic setting (the Indonesian island of Tidore) and its allegorical condemnation of colonialism, but it's the medieval romance which ultimately dominates our attention.

Princess Quisara sets her would-be husbands a task – to rescue her imprisoned brother – in the hope that her lover Ruy Dias will do the honours and claim her hand in reward. She hadn't bargained on the Captain being quite such a wuss, though, and finds herself faced with marriage to a rather more initiative-taking Portuguese soldier, who frees the King with the oldest trick in the book – a fire alarm. Brave words from Armusia win over Quisara's heart, but the hero is incensed by her suggestion that he forsake Christianity and convert to her religion of "maumet Gods" and "wild worships". It's a tantalising insight into Jacobean attitudes to faith and miscegenation, which Fletcher wimps out on exploring much further. Still, Gregory Doran's production thunders along for the most part, the gamelan music and Hindu-style costumes effectively evoking the Asian setting without the need for cumbersome scenery. And he has a strong cast, particularly in Sasha Behar, who plays Quisara like a Cleopatra of the East Indies, and Antony Byrne as the sly, mirthful go-between, Pyniero.

Culture clashes also crop up in Blood Links, William Yang's unexpectedly beguiling performance piece for the start of this year's BITE festival. Yang is third generation Chinese-Australian, gay and has a way with deadpan deliveries. At first, you don't know whether his slide show of distant relatives from around the world is the most boring piece of theatre you're unlikely to stumble upon or some kind of mischievous wind-up. It takes a while for both Yang and the audience to relax into the show, which turns out to be a thoughtful, whimsical and finally moving account of the migrant experience, but also, more generally, about the ineluctable pull of blood bonds, how families "exist in a place that transcends geography".

His photographs are variously banal (the turkey-and-stuffing tableau is a hilariously familiar image of Christmas rituals), intimate, and breathtaking (as Yang remarks on his country of birth: "I have found a spirituality in the Australian landscape that I could not find in the Australian culture").

We laugh when Yang tells us, "You met them at Maureen's Christmas lunch that year", but as he flicks through the family portraits again, you realise that these people no longer feel like strangers.

'Frozen': NT Cottesloe, London SE1 (020 7452 3000), in rep to 24 August; 'The Island Princess': RSC Swan, Stratford-upon-Avon (01789 403403), in rep to 14 September; 'Blood Links': Barbican Pit, London EC2 (020 7638 8891), to Saturday