This is the real Greek, bloody-fantastical thing. After the fascinating but flawed attempt to bring Aeschylus’s Oresteia into the 21st century, the Almeida has turned to a more tradition-conscious kind of experiment with Euripides’ last and greatest masterpiece.

Is there more than one Michael Longhurst? As sometimes happens in theatre, a rising young director seems to be everywhere at once. His calling card is the modestly universal Constellations. Directed with clarity and simplicity, Nick Payne’s romantic two-hander with multiple narratives has travelled from the Royal Court via the West End to New York, before touring the UK and heading back to London this week. Longhurst may need to clone himself in order to be in two places at once: his production of Caryl Churchill’s A Number is also opening at the Young Vic.

There are two fundamental ways to fillet the untranslatable poetry and ritual of Aeschylus, most remote of the three ancient Greek tragedians, for a contemporary audience. One is to find a poet of comparable word-magic and a composer to reflect the crucial role of music at the Athenian festivals, serving the drama with masks and compelling strangeness, as Peter Hall did in his seminal 1980s Oresteia at the National Theatre (poet: Tony Harrison, composer: Harrison Birtwistle, peerless both).

This venue is one of the coolest in London — and its regular audience is both trendy and well-heeled. In the foyer, you get jostled by a better class of person. For this immersive show, written by the prolific and ever-inventive Mike Bartlett, the audience arrives and, after getting its tickets, is divided into four groups: A, B, C and D. Each group is then summoned by tannoy to enter the theatre though a different entrance. Yes, this is not a theatre show — it is a game show.

All that glisters is not gold in the casino and television game-show world of Rupert Goold’s American Shakespeare, first staged by the Royal Shakespeare Company in 2011. Not all the accents are gold either, though working on them only seems to have made a splendid ensemble underline the meaning of every word all the better – and having come straight from the often slapdash verse-speaking of the RSC’s Henry IV, that comes as all the more of an invigorating surprise.

A template of the American theatre gets dusted off to quietly devastating effect in Our Town, the 1938 Thornton Wilder play that has never been especially beloved in Britain even as it gets performed in every high school across the States. With luck, local regard for the work will move up a notch courtesy the UK directorial debut of American actor-director David Cromer, repeating an assignment that brought him extensive plaudits (and a long run) Off Broadway in 2009. Cromer's trump card lies in rendering bruisingly matter-of-fact a piece often dismissed as homespun and folksy.

Dramatic national events such as riots tend to attract verbatim theatre practitioners like smashed shop windows attract looters. In this new play, Alecky Blythe – who specialises in recording ordinary people and editing their words into a humane story – takes to the streets to see what people were saying during the English riots of summer 2011. The main problem at the outset is that citizens armed with new digital media have already filmed and recorded memorable scenes from these events. So does Blythe have anything to add to what we already know?

In creating Mr Burns, Anne Washburn was trying to answer a question overlooked by most purveyors of dystopian fictions: what would happen to pop culture after an apocalypse? The physical and emotional challenges of life after civilisation have been endlessly explored, but very little attention has been paid to the fate of the ever-evolving collection of stories that we carry inside our heads.

Jonathan Kent was an actor before he was a director. Indeed, he had not directed a single play when in his mid-40s he assumed control of the Almeida Theatre in 1990. By the time he and his co-artistic director Ian McDiarmid has left more than a decade later, they had enforced a vital shift in the ecology of London theatre. Kent lured big names to work for small paychecks: Diana Rigg and Ralph Fiennes were soon followed by the likes of Kevin Spacey, Juliette Binoche, Liam Neeson and Cate Blanchett.

The Royal Family: politically irrelevant anachronism? Fodder for tourism? Or enduring symbol of what it means to be British? Mike Bartlett’s shrewd new drama, in a taut, economical and strongly acted production by Rupert Goold, tussles with issues of the limits and shifting values of monarchical power, and with questions of national identity. It has a playfulness that occasionally borders on the glib – yet it also has teeth.