Terence Rattigan’s art of concealment is what makes The Deep Blue Sea so rich and true an observation of the way people behave. Being deprived of his concealing mask is the crucial idea of the interesting new play partnering it at Chichester to mark Rattigan's centenary: Nicholas Wright’s Rattigan’s Nijinsky, which incorporates an unproduced Rattigan TV script into a drama of why it was not produced.

In the spirit in which these reviews are intended, I can report that all the bits of Anne Boleyn are working. The chrome is gleaming; all cylinders are firing. It’ll be good – roadworthy, Globe-worthy – for another year at least.

Imaginative plays that explore the expanses of inner space are all the rage at the Soho Theatre this summer. First there was a superb revival of Anthony Neilson’s Realism, which puts on stage the thoughts of one man during a solitary Saturday, then there was Lou Ramsden’s Hundreds and Thousands, which used a horror-film aesthetic to explore female longing. Now Mongrel Island, which opened last night, looks at the thoughts and emotions of one woman who has a boring office job.

Can journalists write good plays? Sarah Helm has been a Washington correspondent for The Independent during the first Gulf War in 1990, reported from Baghdad in the mid-1990s, and was based in Jerusalem for three years. So her debut play about the Iraq War, which stars Maxine Peake and opened last night, is grounded on a career of watching the Middle East.

Death means learning to say "I love you" in the woozy world of Ghost, the 1990 film that has become a breathlessly vapid musical sure to keep hen parties happy for some while to come (especially now that Dirty Dancing has closed and Flashdance barely got going). The material is cheesy, often defiantly so, and it's here been polished to a high sheen by the director Matthew Warchus and a design team who pull out all the stops in order to snap to attention even the most ADD-afflicted in the house.

Can Thomas Heywood's prosy Jacobean drama of country folk hunting, card playing, screwing around, sliding aristocratically into debt and harrowing one another to death translate successfully to the aftermath of the First World War? Only, perhaps, as edgy semi-farce, towards which Katie Mitchell's nervy, twilit production sometimes veers, not often intentionally. Acting to make you half believe in impossible characters might have saved it. But here you spend less time focusing on the poor puppets who flap around Mitchell's claustrophobic world than looking at the handsome, haunting set.

Situation comedy relies on strong brands, and some ideas just run and run. Yes, Prime Minister is the stage version of the long-running 1980s BBC television shows Yes Minister and Yes, Prime Minister, which memorably starred Nigel Hawthorne and Paul Eddington. First seen at Chichester last year, the play now returns, with a new cast, for a second West End season. But how does this trusty old brand stand up to the stresses and strains of current political life?

Kafka is a bit of a stranger to British stages at the moment, but elsewhere he remains a strong presence. In his short parables, as well as in his classic novels such as The Trial, he conveys a deep understanding of the human condition. But while European postmodern culture might shrug off his insights, he is still close to the heart of some Middle Eastern theatre-makers.

Until quite recently, plays about sport were as rare as British Wimbledon winners. Then, over the past couple of years, came a whole slew of plays about various sports, led by punchy stories about boxing, from Roy Williams’s Sucker Punch to Bryony Lavery’s Beautiful Burnout. Now this growing list of recent fixtures is joined by Wexford-playwright Billy Roche’s bitter-sweet and humorous play, which originally premiered in Dublin in 2008 and opened last night in north London with several Roche veterans in its new cast.

What is a "good" death? How do most of us want to die? These are not questions that we often stop to ask, particularly in the theatre, where deaths tend to be either heroic or sordid. Two years ago, however, the playwright Nell Dunn’s partner of three decades died slowly, painfully, of lung cancer. On his last day he felt as if he were drowning, but of the five NHS professionals who visited him at home, all were trained to prolong life, none to ease the suffering of the dying. Home Death, therefore, is her story, and those of others, about dying at home: good deaths, bad deaths.