Paul, Jan and Louis, three young men living in a gritty part of south London, are bored and broke and, for them, there are two kinds of Britain – one with money and power, and the one they live in, with no money and little to look forward to. No, it's not a play set in 2015, but Barrie Keeffe's Barbarians, set in the mid-1970s when youth unemployment was at an all-time high and the pound was at an all-time low.

Dementia is an increasingly common theme in theatre, television and film. But although there are plenty of stories about old people suffering from Alzheimer’s, what does it feel like to experience this condition? French playwright and novelist Florian Zeller’s Molière Award-winning play – transferring to the West End after highly praised runs at the Tricycle Theatre in north London and the Theatre Royal Bath – attempts an answer by using a sophisticated structure and a deliberately ambiguous method of storytelling.

At the press night curtain call for Richard III, about eleven-and-a half hours after the beginning of this anniversary three-play production, Trevor Nunn stepped in front of his impressively large cast. Not usually a man of few words, this time he uttered only five: "Peter Hall and John Barton".

Titles don’t come much more evocative than this: Valhalla, the gigantic hall in Odin’s Asgard where those slain in battle come to feast, is the Norse mythological version of the Islamist fantasy of eternal life for jihadist martyrs. Valhalla brings to mind the sound of Wagnerian horns and the sights of vast mountain peaks. It’s all very Nordic, very Aryan and very Tolkien.

With her strong, often fierce features and her convincing simulations of rage, Kate Fleetwood might have been born to play Medea. Unfortunately this isn’t Euripides’ Medea but Rachel Cusk’s free variations on the myth rather than the play.

Stop press: our rampant celebrity culture might not be wholly positive! If you’ve already been apprised of that fact some time in the past century, go ahead and skip actor Daniel Dingsdale’s debut play, which – along with Steve Thompson’s similarly outmoded Roaring Trade in the main house – stifles the often creatively programmed Park Theatre’s claim to relevance.

No doubt this sophisticated bagatelle starring Mark Rylance worked like a charm in the intimate space and woody resonance of the Sam Wanamaker Playhouse.

Theatre is in the very bones of this bold adaptation, with the Lyric gifted a cameo role: past productions are fleetingly pastiched in a flashback to the era of the venue’s foundation. Laura Wade and Lyndsey Turner translate the vividly immediate first-person narrative of Sarah Waters’ 1998 novel into a world coloured by the experience of their heroine, whose coming-of-age story is sparked by the stage: make-believe illuminating the truth of her sexual identity.

Entertaining our troops overseas has already proved a fruitful subject for drama, and not only for its show-within-a-show potential. Peter Nichols’ Privates on Parade – revived in the West End three years ago – combined latrine-level banter and tawdry cabaret to create pathos and comedy. Now, updating the military status quo, comes The Sweethearts, a new play by Sarah Page marking the first anniversary of the withdrawal of British troops from Afghanistan.

Iliad is the third collaboration between National Theatre Wales and “the two Mikes”, directorial duo Pearson and Brookes. The pair have been responsible for two previous highlights of the still young company’s back catalogue, The Persians (2010) and Coriolan/us (2012). Aeschylus was re-imagined on a Brecon Beacons military range and Shakespeare recast in an RAF aircraft hangar, so it is perhaps surprising that the ultimate epic drama of war is staged in an actual theatre, the compact and modern Ffwrnes in Llanelli.