You could call it the iceberg syndrome. It’s a work of art that is a flash, a sliver or an imprint: think of a passport photograph, a cheap trinket or a half-finished graffiti. Yet beneath the simple image there is a world of pain. Rachel De-lahay’s new play, a follow up to her award-winning The Westbridge, offers snapshots of the great migrations of recent years, and slowly reveals the raw emotion of these simple tales.

Since his arrival about a decade ago, Dennis Kelly has proved himself to be a master of versatility. He has written in-yer-face shockers such as Osama the Hero and Orphans, elaborate experiments in theatre form such as Love and Money, sprawling epics including The Gods Weep, the paranoid fantasy Utopia for Channel 4 and the deliciously heartwarming Matilda the Musical. Now making his belated debut at the home of British new writing, the question is: which style will he adopt?

There’s a united nations of Great Britain feel about this site-specific Royal Court show: it is a National Theatre of Scotland piece played at the London Welsh Centre as a co-production with the top English new writing company. It’s an entertaining treat — a riotous romp of rhyming couplets, devilish encounters and wild karaoke — curated by Vicky Featherstone, formerly head of the NTS, which premiered the show in Glasgow in 2011, and now supremo of the Royal Court.

With site-specific shows it’s a natural urge to start by reviewing the location. And I’m not strong enough to resist this temptation. So here goes. This new piece by American playwright Annie Baker takes place at the Rose Lipman building in Haggerston, north London. This is a community centre, and first impressions are not encouraging: duck-egg blue walls, dirty windows, faded carpet squares, discoloured ceiling tiles, encrusted neon strips, cluttered notice boards. Don’t go if you feel depressed.

When any arts institution gets a new head, the media scrutiny of their first work is usually intense. The Royal Court theatre’s new artistic director, Vicky Featherstone, has defused this tension by staging not one signature play, but a season of six plays during a festival of other events. Mint, the debut play by director Clare Lizzimore, comes roughly midway through this Open Court season, which has also seen short runs of work by playwrights Lasha Bugadze, Lucas Hnath and Suhayla El-Bushra.

The past: it’s etched into the fabric not just of our lives, but of the architecture that surrounds us – the streets we tread, the buildings where we work or make our homes. In this whimsical, winning 90-minute piece by Will Adamsdale, the past has a niggling habit of leaping out from the places where it should lie buried, rubbing up cheekily against the present, and sticking its nose into the future.

Anthony Neilson is the wild man of new writing. However, this reputation, which has been provoked by shock-fests such as Penetrator (1993) and Stitching (2002), belies the fact that some of his best work, such as The Wonderful World of Dissocia (2004), exudes a warm humanity and offbeat humour. But perhaps the most significant thing about some of his recent work has been his concern with process.

“My honest instinct,” says Jim, the hero of Bruce Norris’s The Low Road, “is one of resentment.” And while this contemporary fable of industrious bees, aka capitalist speculators, is set in the past, and is full of good jokes, it is also laced with emotions that are a tougher sell. Here a humorous tale of a life of entrepreneurship comes hand-in-hand with some satire that is bitter as well as being funny.

Is this the most poetic title in London theatre today? Anders Lustgarten’s new play joins a ragged march of work, from David Hare’s The Power of Yes (2009) to Clare Duffy’s Money: The Gameshow (currently at the Bush Theatre), which attempts to tackle the global financial meltdown. Unlike these other shows, however, it’s USP lies in its claim to offer a solution to the pains and penalties of economic austerity.

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.