London theatre loves plays about the media. Is this because we spend so much time flicking through magazines, visiting websites or watching television? Or is it because this venue’s trendy metropolitan audience is as cynical and world-weary as a media ad buyer? Either way, Lucy Kirkwood’s lively new play is both a hilarious account of lads’ and girls’ mags, and an indictment of their effect on all who come too close to them. But is her argument so obvious that anyone would agree with it?

The famous count could not have a more theatrical pedigree if he tried. The great actor-manager Henry Irving – tall, preternaturally thin, with a fixed glare (due, apparently, to extreme myopia) and a grand manner which gave way, said Bernard Shaw, to "glimpses of a latent bestial dangerousness" – was, said everyone at the time, the obvious source of the Transylvanian Undead aristo as he was created on the page in Dracula by Irving’s business-manager Bram Stoker.

Oh, how it’s raining. Streaming down the windows of the dry goods store, Torrance Mercantile, in the Deep South, where Lady Torrance is marooned in a stiflingly small town and a loveless marriage with an awful secret. Depressing. “We’re under a lifelong sentence to solitary confinement in our own lonely skins,” says 30-year-old drifter Val Xavier in his snakeskin jacket, holding onto his only companion in his wanderings, his precious, celebrity-signed guitar.

Finding the mythic echoes of the ancient Greeks in stories about the modern world is not just confined to past greats such as TS Eliot, but is also used by contemporary adapters of old tragedies. Yet Colin Teevan’s new play, which shadows the lives of Irish navvies working in England with echoes from Greek tragedy, goes one better. Asked by the director Lucy Pitman Wallace to rewrite the Oedipus myth through the lens of Krapp’s Last Tape, the playwright has come up with The Kingdom.

Set at the start of the US and UK invasion of Iraq in 2003, Clare Bayley's Blue Sky follows an old-school journalist pursuing justice at the cost of neighbours and friends. Jane, played with careerist resolve by Sarah Malin, is convinced she has uncovered a case of extraordinary rendition. She believes the CIA are involved in the kidnap of a man seen being bundled on to a private jet in Islamabad so that they can question him under torture. “People,” she says, “don't just disappear.” Now she needs proof.

Still waters run deep, but that truism barely hints at the quiet power of The River, the eagerly awaited new play from Jez Butterworth (writer) and Ian Rickson (director) whose collaboration yet again gives cause for cheer. The converse in almost every way from their immediate Royal Court predecessor, Jerusalem (2009), this latest work is as small-scale, intimate, and compressed as that epoch-defining transfer to the West End and Broadway was rangy, anarchic, and feral.

In the past few years, without any fanfare, the veteran playwright and Spooks script-writer Howard Brenton has not only made a comeback, but also become the chief chronicler of the nation’s past. One year he is telling the story of Harold Macmillan in Never So Good, then he’s doing a version of The Ragged Trousered Philanthropists. He might make a detour to pray with St Paul or to converse with Abelard and Heloise, but then he comes back to English history with the award-winning Anne Boleyn.

If all of Loserville were as arresting and witty as its design, the West End would finally have what it hasn't offered playgoers in years: a buoyant British musical not reliant on a celebrated back catalogue or penned by Andrew Lloyd Webber and his various writing partners over time.

Wow, what a lot of debuts. Adrian Lester (Hustle, Bonekickers, Merlin) makes his Tricycle Theatre debut in this new play about a black actor in Regency London, and it’s written by his wife, the actress Lolita Chakrabarti. The play is her first substantial piece, and it’s also the opener in the new regime of incoming artistic director Indhu Rubasingham, who directs. But is the play, which premiered last night, as redolent of greasepaint and plush curtains as its title implies?

It’s not easy bringing the Mississippi delta to Leeds city centre – yet here its hanging moss and tea-coloured waters fill out every inch of the expansive Quarry stage. Indeed, all that’s missing from Francis O’Connor’s remarkable set is a hungry alligator or two, though in the drama for which it provides a backdrop – Tennessee Williams’s Pulitzer Prize-winning classic about death, desire and deceit – the human characters are capable of inflicting quite enough damage on themselves.