Ari Shaffir: Ari S-P-E-C-T
Heroes @ The Hive, until Aug 28
★★★★✩

What a dude! Nothing is off limits for the former Jerusalem yeshiva student in a well-structured, streetwise and at-times deliciously surreal show.

New Yorker Shaffir, 42, the creator and host of This is not Happening , a storytelling show on the US cable TV network Comedy Central, explores a range of areas in graphic detail, from ladyboys in Thailand to farting on aeroplanes, chlamydia and adoption.

"With adoption, you can shop before you buy: that's prudent," he jests in a broad, rasping accent that originates from Maryland, having dissed the whole concept of having children.

His Jewish material is artfully introduced and after a comic puff around the coffee shops of Amsterdam he goes on a sublimely warped riff about Anne Frank buying a grilled cheese takeaway that is comedy gold.

Tasteless? Self-evidently, but Shaffir's late grandfather was a survivor of the Bergen-Belsen concentration camp and his father Nat was in a work camp and now helps out at the United States Holocaust Memorial Museum in Washington DC. He's a master craftsman of comedy and highly polished black humour.

Woody Allen(ish)
Frankenstein Pub, until Aug 29
★★★★✩

The softly-spoken Simon Schatzberger has brilliantly captured what he calls the "sing-songy and fluctuating" lilt of Woody Allen's slightly whiny Brooklyn accent in this endearing recreation of his 1960s stand-up comedy routines.

Wearing a herringbone tweed jacket, a white shirt, red knitted tie, suede brogues and Argyle socks and the trade-mark Moscot Lemtosh black-framed glasses, Schatzberger, 48, certainly looks the part. They're even the same height at 5ft 6in.

There's also Allen's antique gold pocket watch, which he proudly shows off. "It has great sentimental value for me: my grandfather, on his deathbed, sold it to me," he says wryly.

The Nottingham-born actor, a fan of Allen since he was 16, lovingly picks out his idiosyncratic quirks, such as nervously scratching his head, flicking his glasses with his left hand, and anxiously holding on to the microphone stand as, at first stuttering, he builds up each joke with growing animation to a crescendo, accompanied by self-congratulatory giggles.

There's the classic Moose routine, a favourite of Allen fans, featuring a real moose that comes back from the dead, and the Berkowitzes, a Jewish couple dressed up as a moose for a fancy dress party. And there are less well-known sketches peopled by Sheldon Finkelstein, who tried to bully him as a child, Allen's friend Eggs Benedict who gets a pain in his "chestal area" (cue Woody's hypochondria), and a Ku Klux Klan gang who unwittingly kidnap him when he is dressed as a ghost, going to another costume party.

The timeless stories are more than matched by the Kingston-based actor's affectionate depiction in this sweetly amusing homage.

The Remains of Tom Lehrer (Performed by Adam Kay)
Gilded Balloon Teviot, until Aug 29
★★★✩✩

Adam Kay, the musical comedian, feels an affinity with Tom Lehrer, the "lapsed Jewish" satirical singer-songwriter.

"I'm Jewish-ish. I'm probably on the same level as him," he says, though he points out that while Lehrer went to Harvard University to study mathematics at 15, he had gone to play space games at Lazer Quest.

Kay, 35, who performed his own songs at Prince Harry's 30th birthday party at St James's Palace two years ago and who writes scripted comedy for TV, seeks to impart his passion for the dark humour of the 88-year-old Californian with an almost evangelical fervour.

Parked behind a grand piano, the self-described "lapsed doctor" from Chiswick, west London rattles through the 60-minute set, pared down from the one that sold out in the West End. He packs in about 20 jaunty songs, many of which he has contemporised, including (I'm Spending) Chanucah in Santa Monica.

Kay says: "He realised there were loads of Christmas songs, mostly by Jewish writers, and even as a lapsed Jew he spotted a gap in the market for a Chanucah song."

The show goes down a treat with fellow Tom Lehrer fans - though, for those less in the know, Kay's keenness to cram in as many numbers as he possibly can in an intense manner mitigates against a relaxed appreciation of Lehrer's dark nuggets of gold.