When, earlier this year, Edward Hall took the reins at the Hampstead Theatre, some eyebrows were raised. It’s meant to be a new-writing theatre and Hall has had much more experience directing Shakespeare than in tackling new plays. On the other hand, this venue needed a clean sweep and Hall is certainly able to wield a new broom vigorously. His first show, Shelagh Stephenson’s thrilling play about the disappearance of a gap-year student, opened last night — and it’s an excellent debut.

Theatrical conceits, much like London buses, seem these days to come in threes. Or so it is suggested by the Neil Bartlett/Handspring collaboration Or You Could Kiss Me, the third Cottesloe production this year to peer into the future, albeit only as far as 2036, whereas Mike Bartlett's Earthquakes in London leapt forward to 2525. (Completing the trifecta: Tamsin Oglesby's Really Old, Like Forty Five, set a comparatively imminent 40 years ahead.) And while Oglesby's play featured a robotic nurse, this latest opening puts some very singular puppets centre-stage, alongside a vision of infirmity that could not be either more human - or humane.

The news last week that Michael Grandage will step down next year as artistic director of the Donmar Warehouse feels like one of those moments when an era ends. His ability to programme not only the small Donmar but also to bring excellent productions to the West End — notably Jude Law in Hamlet — is exemplified in the current mini-season at the Trafalgar Studios, which opened last night with American playwright Beau Willimon’s new play about the New Orleans floods of 2005.

There are any number of ways, it's increasingly clear, to approach A Number. Caryl Churchill's astonishingly prismatic and beautiful play about genetic cloning, nature versus nurture and the ineffable mystery of existence as amplified by Shakespeare in a certain well-known tragedy gets its latest London airing this week. To be (happy) or not to be (happy)? That's among the various questions raised in a two-hander (albeit with four characters) that runs less than an hour; any longer than that and your brain just might explode.

It's hard to overestimate the importance of Goethe's Faust to the German soul, though I did once have a German friend who valued George Eliot's Middlemarch more highly. If there's a real English competitor to Goethe in the literary stakes, it is of course Shakespeare, but that doesn't really work either, because, when not thinking of Goethe, many Germans consider Shakespeare neither better nor worse; simply theirs.

Adultery has had a good press recently. Websites such as meet-to-cheat.com, illicitencounters.com and lovinglinks.co.uk have been in the news, and statistics suggest that more of us are being unfaithful than ever before. But although adultery is a staple of farce and mainstream drama, there are few plays that deal with the subject with quite the unsettling ambiguity and disturbing depth that characterise Martin Crimp’s modernistic play, first performed in 2000 and now beautifully revived by the up-and-coming Amelia Nicholson.

Sebastian Faulks’s Birdsong has reached phenomenon status: number 13 on a recent BBC Big Read competition, part of the school curriculum along with World War One poets Wilfred Owen and Siegfried Sassoon, three million copies sold worldwide. Its lyrical, descriptive writing, dense and subtle in detail, consistently moves people to tears.

The business end of 1980s BBC sitcom, the Yes, Minister and Yes, Prime Minister series delivered political body-blows while sporting a dapper suit – satire with a gracious smile. In today’s era of muscled political heavies like The Thick of It, the Jay/Lynn brand of PG humour seems as antiquated as a blunderbuss – particularly when translated to the stage – but with just a few tweaks proves to be surprisingly effective.

When cultural talk drifts toward Mr Big, thoughts tend to turn to Sex and the City's Chris Noth, whose New York is world enough and time away from the doomed metropolis populated by the "big fellah" played by Finbar Lynch in Richard Bean's play of the same name. This big guy is, in fact, slight but menacing: the type of man not unacquainted with the very methods of violence which Harold Pinter, among others, dramatised so well. And when Lynch's Costello remarks, "Unlike you, I am not mentally ill," one sits up and takes notice. The issue here has less to do with what Costello is not and everything to do with what and who he is.

It's the Mousetrap of musicals, the wholly unstoppable show and, to mark its 25th anniversary this year (the 30th, if you date it back to the initial French concept album and Paris production), it will be staged in London at three different venues. You can even see them all in a single, mighty weekend bender, if the mood takes you: the original Les Misérables at the Queen's Theatre, a celebratory all-star concert at the O2 Arena on 3 October and an invigorating new production which plays at the Barbican after a national tour until 2 October.