It’s the end of the world as we know it. At least according to Miles, scientist turned messiah, who lost his son in an accident at a frozen lake, and who experienced visions of an impending apocalypse in his subsequent coma.

He’s established a colony of believers (let’s not call it a cult) in South America, and we’re here to bear witness to the arrival of his estranged wife, intent on reclaiming their daughter back to civilisation.

Rona Munro’s trilogy of plays about Scotland’s Stuart kings premiered at the Edinburgh Festival when Scottish independence was, for many, still a cherished possibility; it transfers to London – within a clarion call of Westminster – just as the promise has been dashed. As timely as the National’s recent Great Britain, the trilogy is more than merely opportune, resonating with the anger and frustration of centuries.

Sofie Gråbøl as Danish royalty: it hardly stretches credulity. The face of Nordic noir has been a star in her home country ever since appearing in Bille August's Pelle the Conqueror in 1987, but is solely familiar on these shores as Sarah Lund, the jumpered Copenhagen detective from three unmissable series of The Killing. This autumn the only thing that will be recognisable about Gråbøl will be those big blue eyes as she is spirited back to the late Middle Ages, bewigged, bejewelled and billowing, to play a queen of Scotland.

Rona Munro's history cycle may take some liberties with the facts, as the writer admits in the programme notes, but its broad narrative sweep has been talked about as a state-of-the-Scottish-nation trilogy. It's the first joint production of the National Theatre of Scotland and the National Theatre and the timing of its premiere at the Edinburgh International Festival couldn't be more pertinent – just a few weeks before Scotland votes on 18 September in the independence referendum.

Flying masonry put the Apollo in the headlines late last year when part of the theatre’s ceiling collapsed; now an airborne vampire and an impressive refurbishment give it new life. A cyclorama of dark tree branches and cloud-scudded skies covers the ongoing repair work overhead.

Site-specific theatre is hard – where to put the audience, can they stand for nearly two hours, how do we enable them to see/hear, most importantly, what is the purpose of the site and how is it to be used? Verbatim theatre, too, is hard – how to shape a narrative, how to develop characters. Put the two genres together, and what have you got? A well-intentioned, rather unfocused mess, to be honest.

Margaret Cho, Assembly ****

Margaret Cho is back, and how. Ten years away from the Fringe, the American-Korean bisexual - “I'm just greedy, I guess” - is a little softer around the edges maybe, but still as funny. With her lefty humour, punctuated by lots of adult content, she is waspish, but definitely not Waspish.

It's a strange thing that boxing, that most dramatic of sports, hasn't been the subject of more plays. It has a protagonist and antagonist, the ring is a ready-made stage, and the sport has thrown up more than its fair share of larger-than-life characters. So, as with buses, when you're waiting for one to come along, two arrive in quick succession; Roy Williams's Sucker Punch, which was at the Royal Court earlier this year, and now the equally brilliant Beautiful Burnout. Comparisons are invidious, so I won't make any, other than to remark that they are two very different beasts.

“All over the world children are safe – but not here, not on my ship.” Despite its wild pack of homeless children, a flesh-eating crocodile and some of the most gut-punching depictions of parental grief in all literature, J M Barrie’s Peter Pan has somehow been consigned to the theatrical remainders bin, its old-fashioned sentimentality acceptable really only at Christmas, or in pantomime form.