Some theatre genres seem indestructible. One of these is the satirical city comedy, for which playwrights dip their pens in poison and spray their venom over the teeming mass of the shallow, the stupid and the successful. When they do this today, they inevitably recall all manner of past plays from Jacobean and Restoration times to Richard Brinsley Sheridan’s The School for Scandal, and beyond. In American Trade, a new play from the immensely talented American playwright Tarell Alvin McCraney, which opened last night, we revisit this familiar territory.

Ben Butley is poisonous, spiteful, a bully, a sadist and a snob. So how does Simon Gray, who created his titular anti-hero in 1971, ensure that an audience can endure his company? He equips him with the kind of lacerating verbal dexterity that makes you catch your breath, appalled and a little awed all at once. And in Lindsay Posner’s fine revival, this nasty, sad, desperate piece of work who, as a lecturer in a London university English department, gets plenty of opportunity to inflict his wit on the soft young sensibilities of eager undergraduates, is played with bilious aplomb by Dominic West. You dislike him, often violently; but you can’t tear your eyes away from him.

With The Cherry Orchard just opened at the National Theatre and The School for Scandal at the Barbican, summer is quickly proving itself the season for classic theatrical revivals. The latest to join the London line-up is Shaw’s perennially beloved comedy of love and the English language, Pygmalion. Debuted at at the Chichester Festival Theatre last July, Philip Prowse’s traditional production returns a year on with a West End home and some starry new cast members, hoping to charm fresh audiences with this oldest of theatrical fairytales.

Anya Reiss must be the most precocious playwright in London. Her 2010 debut, Spur of the Moment, written while she was just 17 and still studying for her A levels, won two Most Promising Playwright awards, from the London Evening Standard and the Critics’ Circle.

Today’s Britons are a minor miracle of globalised taste. Typically, we are amazingly eclectic: we eat curry and sushi, read Swedish novels or South American magic realists, dress like Italians, drive German cars, listen to world music. Our houses are full of Scandinavian design. Our favourite films are as likely to be made in China or Afghanistan as in Hollywood. So, watching the British premiere of a new play by Norwegian Jon Fosse directed by French theatre legend Patrice Chéreau, one is compelled to ask: why are we so suspicious of foreign drama?

British theatre is a bit phobic about travel: you can see plenty of plays set in leafy suburbs, grotty council estates and occasionally in muddy fields, but few that enjoy an overseas setting. And when the Brits do go abroad, they usually follow the well-trodden paths to Africa, the Middle East and north America. But the Royal Court has a different agenda: it works with playwrights abroad and brings their work to Sloane Square so there’s no need to get a visa to experience life in today’s Latvia, as shown in Aleksey Scherbak’s new play, which opened here last night.

Film-maker and playwright Mike Leigh simply doesn’t do revivals. His method of working - which involves a group of actors improvising characters and situations until a story emerges - runs contrary to any notion of returning to a play after its premiere. So it is quite astonishing to report that, for the first time, Leigh has revisited one of his own plays, Ecstasy, which he originally put on at the Hampstead Theatre in September 1979, and which is now back at the same venue.

Recently, some British playwrights have gone back to school, and found that it feels very much like a war zone. All the old tensions between teachers and pupils have escalated into open conflict: knives are drawn, punches thrown and arguments are settled by fights. Likewise, the language is disrespectful at best, and always expletive-heavy. Vivienne Franzmann’s new play, which visits London after opening in Manchester last month, frankly refers to a war zone in its title, and its action is scarcely less antagonistic.

Dave is a bomb, waiting to go off. He’s dangerous because he seems so ordinary. Late-twenties, he’s nothing much to look at. He wears a suit. Works as a civil servant in some absurdly obscure government department. No girlfriend. If truth be told, a bit of a piss-head really. But the thing that makes him dangerous is that - as the title of DC Moore’s 2010 play makes clear - he fancies himself as a truth-teller. He’s painfully honest, and, worse, he uses honesty as a weapon. So when you meet him in a pub, watch out.

At the moment, most of the energy in British new writing seems to be coming from American and Irish playwrights. This is such a regular phenomenon, one that comes around every few years, that it seems idle to speculate on the reasons for it; surely, it’s enough to welcome another new talent from Ireland? As well as being the artistic director of Tall Tales theatre company, Deirdre Kinahan is a prolific playwright. Her UK debut, Moment, opened last night at the Bush Theatre in west London, and is an engrossing study of a dysfunctional family.