Over the past decade or so, Simon Stephens has emerged as one of Britain’s premier playwrights. As well as being a prolific penman, with three volumes of collected plays already in print, he has been tutor on the Royal Court’s Young Writers course and a regular at the National Theatre. He has also enjoyed collaborating with the best directors, one of whom is Marianne Elliott — their version of The Curious Incident of the Dog in the Night-Time transfers to the West End next month.

Rajiv Joseph's Bengal Tiger at the Baghdad Zoo put him in the running for a Pulitzer in 2010. Deservedly so. Set during the Iraq war and featuring a talking tiger (played with verve on Broadway by Robin Williams), it was inventive, funny and profound. Gruesome Playground Injuries is none of these.

It’s like waiting for a number 19 bus. You hang around for half an hour then two come along at once. So it is just now with plays either written by women or featuring women’s lives. While Amelia Bullimore’s sparky three-hander Di and Viv and Rose is storming audiences in Hampstead, Mehmet Ergen, the dynamic Turkish-born founder of both Southwark Playhouse and the Arcola, is continuing to make waves in unfashionable Hackney and Dalston.

There are quite a few laughs in this new adaptation of The Turn of the Screw, Henry James’s chilling and ambiguous novella, written in 1897 after he was told a tale of children possessed by their deceased household servants. As a result I found this production thoroughly entertaining, while appreciating that not all the laughs were intentional.

When feminism was really cool, female playwrights would write flatshare dramas about a group of women, each of whom was representative of a certain way of life. The play title would just be a list of their names. The classic example is Pam Gems’s Dusa, Fish, Stas and Vi from 1976. Does this mean that Amelia Bullmore’s new play, which also has a title listing its female characters, is a trip down nostalgia lane?

On 1 July 1916, the battalion of Lancashire volunteers recruited from Accrington was all but wiped out in about 20 minutes as they took on the task of attacking the village of Serre on the opening day of the Battle of the Somme. Out of 700 men, 235 were killed, 350 wounded, “mown down like meadow grass”. Such was the fate of the Accrington Pals, formally the 11th (Service) Battalion (Accrington) of the East Lancashire Regiment. Some of the lads were as young as 16, inspired by local pride and national patriotism to fib about their age in order to join their mates.

While Kafka specifically declined to indicate exactly what kind of creature Gregor Samsa becomes in his horrific overnight transformation, translators of the novella have gone for a variety of options: bug, beetle, cockroach or vermin. In this stage version, there is no attempt to imitate the appearance of any insect by means of costume or make-up; instead Gísli Örn Garðarsson uses his gymnastic skills to indicate movements alien to human beings while retaining Kafka’s underlying sense of a suffering man trapped in his new body.

David Hare's 1998 play wasn't terribly well received when it was first produced by the Almeida; several critics regarded it as a thin work, weakly directed by Richard Eyre, and opined that Liam Neeson was miscast in the role of Oscar Wilde. Now comes a revival, directed by Australian Neil Armfield that has, on the face of it, dream casting in Rupert Everett as the Irish playwright hounded by the British ruling classes for his homosexuality.

Most of us would love to live in a happy family, but it’s the unhappy ones that make the most compelling drama. And few playwrights do familial tensions as instinctively as Polly Stenham, whose highly successful 2007 debut That Face and 2009 follow-up Tusk Tusk both explored the tensions between parents and children. In her new play, she revisits the mother-son relationship, and adds some thrilling twists to the bubbling brew.

For all its ruminative merits, Richard Vergette's drama is not the “searing political thriller” it purports to be. It raises lots of interesting questions, but they get in the way of any deep emotive power.