Since his arrival about a decade ago, Dennis Kelly has proved himself to be a master of versatility. He has written in-yer-face shockers such as Osama the Hero and Orphans, elaborate experiments in theatre form such as Love and Money, sprawling epics including The Gods Weep, the paranoid fantasy Utopia for Channel 4 and the deliciously heartwarming Matilda the Musical. Now making his belated debut at the home of British new writing, the question is: which style will he adopt?

It’s hard to imagine much upstaging Martyn Jacques, the indomitable falsetto frontman of the Tiger Lillies. The gaping mouth of an enormous mythical fish that seems to have swum straight from the canvases of Hieronymus Bosch, projected right across the stage in their new show Rime of the the Ancient Mariner, comes close.

Shallow in its cartoonish whizz through the tergiversations of a troubled reign, hugely energetic in its language and structured storytelling, Marlowe’s horrible history is never less than compelling and challenging at the National. It may have found its best match yet in the collapsible bric-à-brac pageantry of Joe Hill-Gibbins’ vivid, in-your-face production.

Could you choose between love and knowledge? Between a life of acceptance and affection, and one of self-improvement and learning? These are the questions that Jessica Swale's new play Blue Stockings poses again and again.

It’s as dazzling as a neon-lit cityscape and nearly as sprawling: Lucy Kirkwood’s epic new drama is rich, riveting and theatrically audacious. A co-production with Headlong, the tirelessly inventive touring company founded by Rupert Goold, it feels like an early statement of intent for Goold’s upcoming tenure as artistic director of the Almeida, which begins this September. Fizzing with wit and intelligent ideas, it’s handled with impeccable flair by director Lyndsey Turner. The results are stunning.

Is there such a thing as a gay play? As opposed to a play by a gay writer, or one which has some gay content or is about gay characters. The programme to this atmospheric and moving revival of Alexi Kaye Campbell’s 2008 play contains Edward Albee’s complaint that the gay play is “such an imprecise term”. You can see his point. Whether The Pride is gay or not matters less than the fact that it is an excellent account of self-knowledge, emotional truth and personal honesty.

Sicilian location, Irish populace, Balkan Roma music: Richard Eyre’s production of a Pirandello bagatelle could easily have turned into the kind of Europudding more common in cinema. That it fairly dances over the pitfalls is due partly to a well-calibrated ensemble, but above all to the fact that the great Italian playwright made an exception to social commentary and searching examination of the human condition, coming up instead with a piece of fluff about babymaking village-style.

The Events, Traverse Theatre ****

Britain today: while the total of car crashes is falling the number of whiplash claims is rising by 25 per cent. Yes, the compensation culture is speeding ahead. In Nick Payne’s follow up to his immensely successful West End transfer, Constellations, a firm of personal injury claims lawyers is the setting for a scam in which a money-spinning lie goes wrong. It’s the stuff of many a Newsnight report, but can he make a social issue interesting as a drama?

Over in Southwark you can currently find Rodgers and Hammerstein exploring the seamier side of life among the prostitutes and drop-outs of Pipe Dream, but in the woody amphitheatre of the Regent’s Park Open Air Theatre it’s all raindrops on roses and whiskers on kittens. Nuns, Nazis and singing children are an unlikely recipe for the most wholesome of all family musicals, but against all odds this 1950s classic is still an irrepressible hit – get out of the way or prepare to be reduced to a giddy, ecstatic wreck by a production that will send you home singing.