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.

Banking and the financial world may have gone into free-fall, but there are still killings to be made. Particularly personal ones. Nicholas Pierpan’s You Can Still Make a Killing is a morality tale for our time, a revenge tragedy without corpses, except for reputations. And, in the City, reputation – or rather perception - is everything.

Samuel Beckett recalled sinking into a "whirl of depression" while writing All That Fall. Audiences at this production - those, that is, who have managed to score a ticket for this short, sold-out run - are unlikely to emerge into Jermyn Street in a similarly gloomy frame of mind.

Pity the A-level English student: for them the “rarely seen masterpieces” that creep onto the curriculum and into the theatres. Judging from the frequently giggling reaction of the audience last night of around 100 17- and 18-year-olds, Eugene O’Neill’s tricky tragedy Desire Under the Elms isn’t going to be winning too many A*s among them next summer. Which is a pity, because this is a tough, gnarled play which strips human instincts to their bones. Hatred is its key emotion, loneliness its key condition.

Spain's Golden Age turns unaccountably to dross in Damned by Despair, the Tirso de Molina play that is a good half-hour shorter than the running time given in the programme but won't (in this production, anyway) ever be brief enough for some.