Edinburgh Festival 2019: Sarah Crompton's top shows to see

WhatsOnStage's Sarah Crompton gives us a rundown of her top shows to see at this year's Edinburgh Festivals, both the Fringe and International.

Head to our dedicated Edinburgh festivals page for all the up-to-the minute coverage.

Enough, Traverse Theatre

Stef Smith wrote the lovely, heart-rending Swallow; director Bryony Shanahan has just been appointed to jointly run Manchester's Royal Exchange. Their collaboration on this play about two flight attendants whose lives and friendship start unravelling at 30,000 feet makes this one of the most enticing new works on the Fringe. 1 to 25 August, times vary

Crocodile Fever, Traverse Theatre

A comedy about the reunion of two sisters in rural Northern Ireland in the time of the Troubles sounds worthy of Martin McDonagh or David Ireland. But this one is written by Meghan Tyler, the Traverse's writer in residence, and a woman to watch closely. It's part of the Made in Scotland 2019 showcase and directed by Gareth Nicholls. 2 to 25 August, times vary

Bobby and Amy, Pleasance Courtyard

Another new comedy about an unlikely subject – in this case foot and mouth disease in the late 1990s. Emily Jenkins won a Fringe First for Rainbow in 2012, which was the last time she brought a show to the Festival. Since then she has been slowly honing her craft and building a reputation; this will show how far she has come. She also directs. 31 July to 26 August, 12:45

The Incident Room, Pleasance Courtyard

There's a small sub-set of dramas about real crime at the Fringe this year, of which this sounds the most intriguing. Set in the Millgarth Incident Room, epicentre of the hunt to catch the man known as the Yorkshire Ripper, in 1975, it follows a young female sergeant as she joins the team. Created by New Diorama, who also made Secret Life of Humans and Down and Out in Paris and London, it has impeccable credentials. 31 July to 26 August, 16:30

La Reprise, Histoire(s) du Theatre, The Lyceum

Europe's hottest director Milo Rau's show is the undoubted highlight of the International Festival. It's based around the shocking torture and death of a young man that shocked Belgium; both an investigation of the death and an enquiry into the origins of theatrical tragedy, it comes blazing clouds of glory from its tour of festivals around the world. 3 to 5 August, 20:00 (14:00 on 4 August)

Oedipus, International Festival, King's Theatre

Robert Icke's breakthrough production was his version of Oresteia, a free adaptation of the original. Now he returns to Greek ground, with the exceptional ensemble of Internationaal Theater Amsterdam, which turns the Oedipus of Sophocles into a thriller in real time, transforming Oedipus into a political giant of today. 14 to 17 August, 20:00 (15:00 on 17 August)

Red Dust Road, The Lyceum

Tanika Gupta's adapts Jackie Kay's memoir about her 20-year search for her biological mother and father in this production from the National Theatre of Scotland and HOME. The poet, novelist and Scottish makar grew up in Glasgow in the 1970s and her story is compelling; the show, part of the International Festival and directed by Dawn Walton, shows every sign of being equally absorbing. 14 to 18 August, times vary

Cardboard Citizens: Bystanders, Summerhall

It's impossible to ignore the rise of homelessness on our streets, so it is good to see the stories of homeless men and women expanded and explained. This committed company returns to Edinburgh with a collection of tales from a Windrush generation boxer, a Polish migrant and a man with a bottle of gin and a television in his shopping trolley. 31 July to 25 August, 11:30

On the Other Hand, We're Happy, Summerhall, Roundabout

In the consistently excellent Paines Plough at Roundabout season, Daf James' play about a single father meeting his adopted daughter for the first time – and then agreeing to meet her birth mother – looks particularly appealing. It's a co-production with Theatr Clwyd and directed by Stef O'Driscoll. 31 July to 24 August, times vary

Eddie Izzard: Expectations of Great Expectations, Assembly, George Square

I always associate Edinburgh with Eddie Izzard ever since I (accidentally) met him running up Arthur's Seat on one of his many marathons. This year he's back on stage, performing his work in progress based on Charles Dickens' sprawling novel. It is certain to be something. 7 to 25 August, times vary