It’s brave to take Shakespeare into the West End in midsummer – and in this of all summers. Greg Doran’s all-black, African Caesar certainly doesn’t lack for impact, colour, zest, urgency. It takes the audience by the scruff of the neck and rams the play down our throats. The concept is impressive. The set, half Roman amphitheatre, half Nazi bunker dominated by a giant effigy, its back towards us with arm raised in totemic salute, summons up TV images of dictators who eventually come crashing down, from Stalin to Mubarak and who knows how many more to come.

Is it the greatest story ever told, or the most indulgent nativity ever staged? The return of the York Mystery Plays – this summer’s blue-ribbon theatrical spectacular in the North – begins by beguiling, ends up bemusing, while in between is a sacred story about the eternal battle of good and evil, from Creation to the Last Judgement. The show’s subject matter is as epic as its telling, which involves more than 1700 volunteers (including 500 cast members) and takes place in the ruins of St Mary’s Abbey. It is the UK’s largest outdoor theatre production this year.

Rosie Wilby: How (Not) to Make it in Britpop, Bongo Club ***

In the 1990s Rosie Wilby was lurking on the outer edges of Britpop with her band Wilby, whose giddy career highlights included opening for Tony Hadley (he evacuated the entire room for the soundcheck), being clamped outside the venue while supporting Bob Geldof, and getting their own plastic name tag in the racks of Virgin Megastore.

National Theatre Wales like the word “us”. It was there in Michael Sheen’s Passion of Port Talbot – its film adaptation was called The Gospel of Us – and it is here, prominently, in the multi-layered title of Mike Pearson and Mike Brookes’ latest site-specific offering. The team that brought Aeschylus’ The Persians to the Brecon Beacons military range have now commandeered a disused aircraft hangar a few miles outside Cardiff to stage an experimental version of Shakespeare’s Coriolanus, sprinkled with Bertolt Brecht’s unfinished version Coriolan.

The curators encourage you to come to Bush Bazaar with an open mind to explore the value of theatre. But I found this cluttered evening a lesson in the value of saying no. Twenty companies – 100 emerging artists in all – have taken over the building to sell their wares, including a dinner party, a cleansing treatment and one to one with Justin Bieber (hard to resist). After paying £10 to get in, you decide what to see and how much more to pay the artists. Sometimes before their show.

When Complicite conceived their beautiful A Disappearing Number they gave maths energy, drama, and above all watchability, but they never quite brought the heart. In Simon Stephens’s new adaptation, A Curious Incident of the Dog in the Night-Time has it in abundance (as well of course as a dead bee, a live rat, three beer cans and 20-odd metres of model train-track). When you can persuade an audience to stay behind after the curtain-call for a mini maths tutorial you’re doing something right; when you can reduce them to tears with it you’re doing something miraculous.

Philadelphia, Here I Come! ends in its Donmar invocation with the roar of a plane taking off, which only amplifies one’s sense that the show has taken some while to take wing. Markedly better after the interval than during an abrasive first half, the director Lindsey Turner’s determinedly unsentimental take on Brian Friel’s breakthrough 1964 play comes at a price, and some may wonder whether the (very real) pay-off is worth the often snarky ride getting there.

Britain may be in grip of Olympic fever, but two playwrights are questioning our unqualified cheer: should we really break out into an excited sweat, they ask, at the mention of beach volleyball, Rebecca Adlington and Danny Boyle? Taking Part and After the Party come under the umbrella of Playing the Games, which comprises a fortnight of plays, standup and talks at the Criterion Theatre responding to London 2012. Although complementary, each one-hour comic play stands alone.

Adrian Burley MP would probably call In Water I’m Weightless “leftie multicultural crap”. I’d like to bestow similar praise. In common with Danny Boyle’s Olympic opening ceremony, director John McGrath’s exploration of issues facing disabled people is a bit of a mess, a bit of a tick-box exercise and thoroughly enjoyable.

“Would you enforce me to a world of cares?” croons Rylance’s Richard III, lingering tremulously over his question, the picture of world-sick piety and reluctance. As the groundlings cheer an ecstatic affirmative, Shakespeare’s most compelling villain once again claims the dramatic victory. History may have him as the vanquished, but in Tim Carroll’s new Globe production, even death cannot strip the crown of the vanquisher from Mark Rylance’s brow.