They’re eating out of the palm of his hand. Or so he thinks. Stephen Bellamy is a spin doctor, only 25 years old but already a hotshot in American electioneering. At the off, in Beau Willimon’s fictionalised drama about modern-day Machiavels, Bellamy is presuming to manipulate the press, in Iowa's primary, with hubristic confidence. Two Democratic presidential candidates are going head-to-head. It's Morris versus Pullman and, in order to keep Morris leading in the polls, Bellamy and his boss – the campaign manager, Paul Zara – are about to dish some dirt on Pullman, without any qualms.

In playwriting, there’s near-perfection, perfection and oh-my-God-how-I-wish-I’d-written-that. Terry Johnson’s Hysteria, which was first staged at the Royal Court 20 years ago, is definitely in the OMG category. Subtitled “Fragments of an Analysis of an Obsessional Neurosis”, it is now a contemporary classic, and deservedly so. Both a demented farce and a serious study of psychoanalytical theory, both surrealistic and feminist, both arty and troubling, it is also a fantastically brilliant entertainment.

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 ****