“Another Op'nin', Another Show”. The first musical number of Cole Porter's Kiss Me, Kate sets the scene for a group of actors and hoofers to brush up their Shakespeare, cross their fingers and hold on to their hearts, and to hope that not too much goes wrong with their show in late 1940s Baltimore. This BBC Proms performance was anything but that kind of on-the hoof creation: it was meticulously planned, ambitiously resourced, staged and choreographed, with costume changes a-plenty.

The latest production of Tennessee Williams’s sultry, brutal yet poetic masterpiece is mainstream theatre that dares to go out on a limb. Directed by Benedict Andrews, it may occasionally miss a beat, but its risk-taking comes with an innate sense of the play’s scorching pathos and an unnerving, dare one say exhilarating taste for the jugular that matches that of its primal male.

It should work as pure musical theatre. Yet what precisely is Gershwin’s - or rather “The Gershwins’”, as this title frames it, though Ira wasn’t quite Gilbert or Brecht - Porgy and Bess? An opera? Trevor Nunn made the three-hour-plus score, much cut here, dazzle at Glyndebourne and Covent Garden. Michael Tilson Thomas’s Barbican espousal of bleeding chunks alongside Berg’s Lulu, left as a torso in the year of Porgy’s premiere, 1935, even put me in mind of the sheer generous optimism of Wagner’s Die Meistersinger. A musical?

The pivotal early 1930s period in which Herr Hitler overcame strong if fractured left-wing opposition should make for meaty drama, but the sluggish polemic currently occupying Southwark Playhouse will leave carnivorous viewers unsatiated. American playwright Tony Kusher is rightly celebrated for his Pulitzer Prize-winning Angels in America, which combines urgent social issues with a moving portrait of humanity, but his earlier work A Bright Room Called Day only hints at that remarkable skill.

The work of William Inge doesn't get much of a look-in on British stages, but the American dramatist's depictions of frustrated aspirations and desires at work in small-town Midwestern lives - most famously realised in the Pulitzer-winning Picnic and Bus Stop - received major Broadway productions in the 1950s. Natural Affection is a later work dating from 1962 which foundered partly due to a New York City newspaper strike, not re-emerging until an Off Broadway run last autumn.

There is so much public anxiety about paedophiles on the internet that it’s surprising that so few plays tackle the issue. Now Los Angeles playwright Jennifer Haley brings her new play on the subject, which won the 2012 Susan Smith Blackburn Prize, to London after winning awards in the States.

“Comedy, and a bit with a dog.” That’s what audiences really want according to the hapless would-be impresario Mr Henslowe, and that’s certainly what they get in Lee Hall’s new stage adaptation of John Madden’s 1998 film Shakespeare in Love – several bits with a dog, in fact.

While it is something of a cliché to be reminded that forgetting the past is a sure way of repeating it, the problems of the Middle East are so acute that this thought might be worth taking seriously. In Holy Warriors, playwright David Eldridge’s new look at the struggle for Jerusalem and the Holy Land from the Middle Ages to the present day, the scope is ambitious and the subject matter as timely as can be. But is the play any good?

We know how the story ends, but then so did Euripides' first audience in Athens in 431 BC. Medea was already a familiar character of myth, a sorceress whose ungovernable passion for Jason led her to commit horrible murders when he abandoned her for another woman. Now, as in the Golden Age of Greek drama, the chief interest is in the way the tale is told. And the National Theatre has assembled quite a team for the purpose.

“Some might say we’re getting too old for this sort of thing,” declares Martin Jarvis’s Jack Worthing, going off Wlldean piste. Well, we did wonder whether the reunion of Jarvis with Nigel Havers’s Algernon after 32 years might not be some sort of vanity Earnest. But you can trust director Lucy Bailey to make sense not only of “the boys” but also their mature objects of desire, not to mention a Lady Bracknell (Siân Phillips, flawless, pictured below) who at an astonishing 81 is past having a daughter of marriageable age.